Algorithm 447: efficient algorithms for graph manipulation

Lecture Notes in Computer Science, 2011

The architecture of a software system is typically defined as the organization of the system, the relationships among its components and the principles governing their design. By including artifacts coresponding to software engineering processes, the definition gets naturally extended into the architecture of a software system and process. In this paper we propose a holistic model to organize knowledge of such architectures. This model is graph-based. It collects architectural artifacts as vertices and their relationships as edges. It allows operations like metric calculation, refactoring, bad smell detection and pattern discovery as algorithmic transformations on graphs. It is independent of development languages. It can be applied for both formal and adaptive projects. We have implemented prototype tools supporting this model. The artifacts are stored in a graph database. The operations are defined in a graph query language. They have short formulation and are efficiently executed by the graph database engine.

SIAM Journal on Computing, 1989

We assume a parallel RAM model which allows both concurrent reads and concurrent writes of a global memory.

Physical Review E, 2014

We study the mutual percolation of a system composed of two interdependent random regular networks. We introduce a notion of distance to explore the effects of the proximity of interdependent nodes on the cascade of failures after an initial attack. We find a non-trivial relation between the nature of the transition through which the networks disintegrate and the parameters of the system, which are the degree of the nodes and the maximum distance between interdependent nodes. We explain this relation by solving the problem analytically for the relevant set of cases.

Lecture Notes in Computer Science, 2014

In this paper we present an original approach for community detection in complex networks. The approach belongs to the family of seed-centric algorithms. However, instead of expanding communities around selected seeds as most of existing approaches do, we explore here applying an ensemble clustering approach to different network partitions derived from ego-centered communities computed for each selected seed. Ego-centered communities are themselves computed applying a recently proposed ensemble ranking based approach that allow to efficiently combine various local modularities used to guide a greedy optimization process. Results of first experiments on real world networks for which a ground truth decomposition into communities are known, argue for the validity of our approach.

Quantum Information Processing, 2011

Traditional tree search algorithms supply a blueprint for modeling problem solving behaviour. A diverse spectrum of problems can be formulated in terms of tree search. Quantum computation, in particular Grover's algorithm, has aroused a great deal of interest since it allows for a quadratic speedup to be obtained in search procedures. In this work we consider the impact of incorporating classical search concepts alongside Grover's algorithm into a hybrid quantum search system. Some of the crucial points examined include: (1) the reverberations of contemplating the use of non-constant branching factors; (2) determining the consequences of incorporating an heuristic perspective into a quantum tree search model.

Communications in Computer and Information Science, 2011

Enterprise Application Integration (EAI) is a field of Software Engineering. Its focus is on helping software engineers integrate existing applications at a sensible costs, so that they can easily implement and evolve business processes. EAI solutions are distributed in nature, which makes them inherently prone to failures. In this paper, we report on a proposal to address error detection in EAI solutions. The main contribution is that it can deal with both choreographies and orchestrations and that it is independent from the execution model used.

PLOS ONE, 2016

Profile Hidden Markov Model (Profile-HMM) is an efficient statistical approach to represent protein families. Currently, several databases maintain valuable protein sequence information as profile-HMMs. There is an increasing interest to improve the efficiency of searching Profile-HMM databases to detect sequence-profile or profile-profile homology. However, most efforts to enhance searching efficiency have been focusing on improving the alignment algorithms. Although the performance of these algorithms is fairly acceptable, the growing size of these databases, as well as the increasing demand for using batch query searching approach, are strong motivations that call for further enhancement of information retrieval from profile-HMM databases. This work presents a heuristic method to accelerate the current profile-HMM homology searching approaches. The method works by cluster-based remodeling of the database to reduce the search space, rather than focusing on the alignment algorithms. Using different clustering techniques, 4284 TIGRFAMs profiles were clustered based on their similarities. A representative for each cluster was assigned. To enhance sensitivity, we proposed an extended step that allows overlapping among clusters. A validation benchmark of 6000 randomly selected protein sequences was used to query the clustered profiles. To evaluate the efficiency of our approach, speed and recall values were measured and compared with the sequential search approach. Using hierarchical, kmeans, and connected component clustering techniques followed by the extended overlapping step, we obtained an average reduction in time of 41%, and an average recall of 96%. Our results demonstrate that representation of profile-HMMs using a clustering-based approach can significantly accelerate data retrieval from profile-HMM databases.

This work addresses the problem of assigning a set of long reads issued from a de novo transcriptomics study to clusters by genes they originate from. The different transcripts of a gene give long reads sharing similar sequences and our work makes use of this fact to retrieve the right cluster of reads for each gene from the graph of similarity between reads. We propose a method based on the use of the clustering coefficient (CC) and the search of a minimal cut in the graph with a greedy procedure favoring nodes with a high degree and high CC. Our approach compares favorably to state of the art methods. We provide results on the mouse brain transcriptome which show that the approach achieves a high precision level and a good level of recall despite not using any reference genome.

Mathematics

Given a multivariate complex centered Gaussian vector Z = ( Z 1 , ⋯ , Z p ) with non-singular covariance matrix Σ , we derive sufficient conditions on the nullity of the complex moments and we give a closed-form expression for the non-null complex moments. We present conditions for the factorisation of the complex moments. Computational consequences of these results are discussed.

Mathematics

The principal aim of this article is to initiate a study of the following coloring notion for digraphs. An odd k-edge coloring of a general digraph (directed pseudograph) D is a (not necessarily proper) coloring of its edges with at most k colors such that for every vertex v and color c holds: if c is used on the set ∂D(v) of edges incident with v, then c appears an odd number of times on each non-empty set from the pair ∂D+(v),∂D−(v) of, respectively, outgoing and incoming edges incident with v. We show that it can be decided in polynomial time whether D admits an odd 2-edge coloring. Throughout the paper, several conjectures, questions and open problems are posed. In particular, we conjecture that for each odd edge-colorable digraph four colors suffice.

Information Processing Letters, 1987

A dynamic connectivity problem consists of an initial graph, and a sequence of operations consisting of graph modifications and graph connectivity tests. The size n of the problem is the sum of the maximum number of vertices and edges of the derived graph, plus the number of operations to be executed. Each graph modification is a deletion of either an edge or an isolated vertex. Each graph connectivity test is to determine if there exists a path in the current graph between two given vertices (the vertices can vary for distinct tests). The best previously known time for this dynamic connectivity problem was ~(n2). Our main result is an O(ng + n log n) time algorithm for the dynamic connectivity problem in the case of the maximum genus of the derived graph being g.

Information Processing Letters, 1985

This paper concerns the computational complexity of depth-first search. Suppose we are given a rooted graph G with fixed adjacency lists and vertices u, v. We wish to test if u is first visited before v in depth-first search order of G. We show that this problem, for undirected and directed graphs, is complete in deterministic polynomial time with respect to deterministic log-space reductions. This gives strong evidence that depth-first search ordering can be done neither in deterministic space (log n) c nor in parallel time (log n) c, for any constant c > 0.

Handbook of Combinatorial Optimization, 2013

This chapter considers the following problem of computing a map of geometric minimal cuts (called MGMC problem): Given a graph G = (V, E) and a planar embedding of a subgraph H = (VH , EH) of G, compute the map of geometric minimal cuts induced by axis-aligned rectangles in the embedding plane. The MGMC problem is motivated by the critical area extraction problem in VLSI designs and finds applications in several other fields. This chapter surveys two different approaches for the MGMC problem based on a mix of geometric and graph algorithm techniques that can be regarded complementary. It is first shown that unlike the classic min-cut problem on graphs, the number of all rectilinear geometric minimal cuts is bounded by a low polynomial, O(n 3). Based on this observation, the first approach enumerates all rectilinear geometric minimal cuts and computes their L∞ Hausdorff Voronoi diagram, which is equivalent to the L∞ Hausdorff Voronoi diagram of axis aligned rectangles. The second approach is based on higher order Voronoi diagrams and identifies necessary geometric minimal cuts and their Hausdorff Voronoi diagram in an iterative manner. The embedding in the latter approach includes arbitrary polygons. This chapter also presents the structural properties of the L∞ Hausdorff Voronoi of rectangles that provides the map of the MGMC problem, and plane sweep algorithms for its construction. 1 Introduction This chapter considers the following problem, called Map of Geometric Minimal Cuts (MGMC): Given a graph G = (V, E) and a planar embedding of a subgraph

Physical Review Letters, 2008

A common definition of a robust connection between two nodes in a network such as a communication network is that there should be at least two independent paths connecting them, so that the failure of no single node in the network causes them to become disconnected. This definition leads us naturally to consider bicomponents, subnetworks in which every node has a robust connection of this kind to every other. Here we study bicomponents in both real and model networks using a combination of exact analytic techniques and numerical methods. We show that standard network models predict there to be essentially no small bicomponents in most networks, but there may be a giant bicomponent, whose presence coincides with the presence of the ordinary giant component, and we find that real networks seem by and large to follow this pattern, although there are some interesting exceptions. We study the size of the giant bicomponent as nodes in the network fail, using a specially developed computer algorithm based on data trees, and find in some cases that our networks are quite robust to failure, with large bicomponents persisting until almost all vertices have been removed.

Physical Review E

An articulation point (AP) in a network is a node whose deletion would split the network component on which it resides into two or more components. APs are vulnerable spots that play an important role in network collapse processes, which may result from node failures, attacks, or epidemics. Therefore, the abundance and properties of APs affect the resilience of the network to these collapse scenarios. Here we present analytical results for the statistical properties of APs in configuration model networks. In order to quantify the abundance of APs, we calculate the probability P (i ∈ AP) that a random node, i, in a configuration model network with a given degree distribution, P (K = k), is an AP. We also obtain the conditional probability P (i ∈ AP|k) that a random node of degree k is an AP and find that high-degree nodes are more likely to be APs than lowdegree nodes. Using Bayes's theorem, we obtain the conditional degree distribution, P (K = k|AP), over the set of APs and compare it to the overall degree distribution P (K = k). We propose a centrality measure based on APs: Each node can be characterized by its articulation rank, r, which is the number of components that would be added to the network upon deletion of that node. For nodes which are not APs, the articulation rank is r = 0, while for APs it satisfies r 1. We obtain a closed-form analytical expression for the distribution of articulation ranks, P (R = r). Configuration model networks often exhibit a coexistence between a giant component and finite components. While the giant component is extensive in the network size and exhibits cycles, the finite components are nonextensive tree structures. To examine the distinct properties of APs on the giant and on the finite components, we calculate the probabilities presented above separately for the giant and the finite components. We apply these results to ensembles of configuration model networks with degree distributions that follow a Poisson distribution (Erdős-Rényi networks), an exponential distribution of the form P (K = k) ∼ e −αk , and a power-law distribution of the form P (K = k) ∼ k −γ (scale-free networks), where k k min = 1. The implications of these results are discussed in the context of common attack scenarios and network dismantling processes.

Genes

RNA molecules are composed of modular architectural units that define their unique structural and functional properties. Characterization of these building blocks can help interpret RNA structure/function relationships. We present an RNA secondary structure motif and submotif library using dual graph representation and partitioning. Dual graphs represent RNA helices as vertices and loops as edges. Unlike tree graphs, dual graphs can represent RNA pseudoknots (intertwined base pairs). For a representative set of RNA structures, we construct dual graphs from their secondary structures, and apply our partitioning algorithm to identify non-separable subgraphs (or blocks) without breaking pseudoknots. We report 56 subgraph blocks up to nine vertices; among them, 22 are frequently occurring, 15 of which contain pseudoknots. We then catalog atomic fragments corresponding to the subgraph blocks to define a library of building blocks that can be used for RNA design, which we call RAG-3Dual, ...

Lecture Notes in Computer Science, 2008

The increasing growth of data on protein-protein interaction (PPI) networks has boosted research on their comparative analysis. In particular, recent studies proposed models and algorithms for performing network alignment, the comparison of networks across species for discovering conserved modules. Common approaches for this task construct a merged representation of the considered networks, called alignment graph, and search the alignment graph for conserved networks of interest using greedy techniques. In this paper we propose a modular approach to this task. First, each network to be compared is divided into small subnets which are likely to contain conserved modules. To this aim, we develop an algorithm for dividing PPI networks that combines a graph theoretical property(articulation) with a biological one (orthology). Next, network alignment is performed on pairs of resulting subnets from different species. We tackle this task by means of a state-of-the-art alignment graph model for constructing alignment graphs, and an exact algorithm for searching in the alignment graph. Results of experiments show the ability of this approach to discover accurate conserved modules, and substantiate the importance of the notions of orthology and articulation for performing comparative network analysis in a modular fashion.

Algorithmica, 2014

HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Optimization Letters, 2015

In several economical, statistical and geographical applications, a territory must be subdivided into functional regions. Such regions are not fixed and politically delimited, but should be identified by analyzing the interactions among all its constituent localities. This is a very delicate and important task, that often turns out to be computationally difficult. In this work we propose an innovative approach to this problem based on the solution of minimum cut problems over an undirected graph called here transitions graph. The proposed procedure guarantees that the obtained regions satisfy all the statistical conditions required when considering this type of problems. Results on real-world instances show the effectiveness of the proposed approach.

2021

We investigate the statistics of articulation points and bredges (bridge edges) in complex networks in which bonds are randomly removed in a percolation process. Because of the heterogeneous structure of a complex network, the probability of a node to be an articulation point or the probability of an edge to be a bredge will not be homogeneous across the network. We therefore analyze full distributions of articulation point probabilities as well as bredge probabilities, using a message-passing or cavity approach to the problem. Our methods allow us to obtain these distributions both for large single instances of networks and for ensembles of networks in the configuration model class in the thermodynamic limit, through a single unified approach. We also evaluate deconvolutions of these distributions according to degrees of the node or the degrees of both adjacent nodes in the case of bredges. We obtain closed form expressions for the large mean degree limit of Erdős-Rényi networks. M...

Nature Methods, 2013

We describe an algorithm for phasing protein crystal X-ray diffraction data that identifies, retrieves, refines and exploits general tertiary structural information from small fragments available in the Protein Data Bank. The algorithm successfully phased, through unspecific molecular replacement combined with density modification, all-helical, mixed alpha-beta, and all-beta protein structures. The method is available as a software implementation: Borges. Main With structural knowledge available of the over 80,000 macromolecular crystal structures recorded in the Protein Data Bank (PDB) 1 , it should be feasible to solve the 'crystallographic phase problem' for any new structure through computation 2. The crystallographic phase problem arises because only the diffracted intensities and not the phases are determined from the X-ray diffraction experiment, but the missing phases are essential to compute the structure. Initial phases are usually derived from measurement of heavy atom or anomalous scatterer derivatives, which involves an increase in the experimental effort and timescale of the crystallographic study, as many derivatives turn out to be unsuccessful. Molecular replacement phasing 3, 4 , on the other hand, works by locating a related model within the crystallographic unit cell to best account for the experimental diffraction data. Typically, homologs for molecular replacement are retrieved by finding closely related sequences. More recently, molecular replacement using remote homologs has been made successful by combining modeling with the program Rosetta 5. This requires composing a fairly complete structural hypothesis within a 1.5-Å r.m.s. deviation from the true structure. Alternatively, as little as 10% of the total mainchain structure is enough to achieve phasing at 2-Å resolution, provided that it is almost identical to part of the target structure and accurately placed (r.m.s. deviation <0.5 Å) 6. Our previous program ARCIMBOLDO 6 , for ab initio phasing from the native data alone, combines fragment location with Phaser 7 and density modification and autotracing with SHELXE 8 in a supercomputing environment 9. By applying secondary-structure constraints and density modification 10 , it overcomes the resolution and size limitations of direct methods based on constraints derived from atomicity 11. By sequentially searching for polyalanine helices, ARCIMBOLDO generates hypotheses without specific previous structural knowledge that, if close enough to the true structure, can be expanded to a full solution. The limiting condition is that the search for the first fragment must contain a correct solution; this becomes increasingly challenging for larger structures as the signal becomes weaker. One possible solution is to locate larger, composite fragments, by using tertiary rather than secondary structure. In this particular scenario, modeling has limited use, as both the sequence and the context of the fragment are unknown and optimization would be largely underdetermined. We describe an algorithm and software tool, Borges (http://chango.ibmb.csic.es/BORGES/), that uses tertiary-structure searching in the PDB to solve the crystallographic phase problem. The PDB contains a vast amount of information, and for any unknown structure, given small enough fragments (for example, two helices or three strands in a particular configuration), close geometrical models are bound to occur in some of the deposited entries. In analogy to Jorge Luis Borges' "Library of Babel" that enclosed books with all random combinations of letters and therefore held any possible book, we reasoned that the information to solve the phase problem is already present in the PDB. All the more so, as unlike the Library of Babel, the PDB is nonrandom, containing in all sorts of structural contexts only the structural units that are stable enough to exist. Further, our method requires small 'sentences' instead of 'volumes', that is, a small fraction of perfect mainchain rather than a complete description of the structure. Borges runs on a workstation that automatically accesses and distributes calculations to a cluster or supercomputer (Online Methods). Existing tools to analyze and retrieve structural information 12 are meant to identify overall, rather than local, geometry or focus on libraries to be exploited in conventional molecular replacement 13 , model building and map interpretation 14 and refinement 15 .

Journal of Heuristics

In this paper we propose a new problem of finding the maximal biconnected partitioning of a graph with a size constraint (MBCPG-SC). With the goal of finding approximate solutions for the MBCPG-SC, a heuristic method is developed based on the open ear decomposition of graphs. Its essential part is an adaptation of the breadth first search which makes it possible to grow bi-connected subgraphs. The proposed randomized algorithm consists of growing several subgraphs in parallel. The quality of solutions generated in this way is further improved using a local search which exploits neighboring relations between the subgraphs. In order to evaluate the performance of the method, an algorithm for generating pseudo-random unit disc graphs with known optimal solutions is created. The conducted computational experiments show that the proposed method frequently manages to find optimal solutions and has an average error of only a few percent to known optimal solutions. Further, it manages to find high quality approximate solutions for graphs having up to 10.000 nodes in reasonable time.

Journal of Combinatorial Optimization

A reassembling of a simple graph G = (V, E) is an abstraction of a problem arising in earlier studies of network analysis [2, 7, 8, 14]. There are several equivalent definitions of graph reassembling; in this report we use a definition which makes it closest to the notion of graph carving. A reassembling is a rooted binary tree whose nodes are subsets of V and whose leaf nodes are singleton sets, with each of the latter containing a distinct vertex of G. The parent of two nodes in the reassembling is the union of the two children's vertex sets. The root node of the reassembling is the full set V. The edge-boundary degree of a node in the reassembling is the number of edges in G that connect vertices in the node's set to vertices not in the node's set. A reassembling's α-measure is the largest edge-boundary degree of any node in the reassembling. A reassembling of G is α-optimal if its α-measure is the minimum among all α-measures of G's reassemblings. The problem of finding an α-optimal reassembling of a simple graph in general was already shown to be NP-hard [10, 11, among others]. In this report we present an algorithm which, given a 3-regular plane graph G = (V, E) as input, returns a reassembling of G with an α-measure independent of n = | V | and upper-bounded by 2k, where k is the edge-outerplanarity of G. (Edge-outerplanarity is distinct but closely related to the usual notion of outerplanarity; as with outerplanarity, for a fixed edge-outerplanarity k, the number n of vertices can be arbitrarily large.) Our algorithm runs in linear time O(n). Moreover, we construct a class of 3-regular plane graphs for which this α-measure is optimal, by proving that 2k is the lower bound on the α-measure of any reassembling of a graph in that class. 1. For every v ∈ V , the singleton set {v} is in B. These are the n leaf nodes of B. 2. The full set V is in B. This is the root node of B. 3. Every node X ∈ B − {V } other than the root has a unique sibling Y ∈ B − {V } such that: X ∩ Y = ∅ and (X ∪ Y) ∈ B. This is a property of every of the (2n − 2) nodes that are not the root. We also call B a binary reassembling of V , or also a binary reassembling of G when V = V(G). 4 To denote the reassembling of graph G according to B, we write (G, B). Depending on the context, we may refer to the nodes of B as vertex clusters of G. 5 If X and Y are disjoint subsets of V(G), we write ∂ G (X, Y) to denote the set of all edges connecting X and Y , each such edge with one endpoint in X and one endpoint in Y : ∂ G (X, Y) { v w ∈ E(G) | v ∈ X and w ∈ Y }. If G is clear from the context, we just write ∂ (X, Y). We also write ∂ (X) to denote ∂ (X, E(G) − X). There are different ways of optimizing the reassembling of G, depending on the measure we choose on it. For X ⊆ V(G), the edge-boundary size of X in G is ∂ G X | ∂ G (X) |. If G is clear from the context, we write ∂ X instead of ∂ G X. If X is a singleton set {v}, then ∂ {v} is simply deg (v), the degree of v. What we 2 http://cs-people.bu.edu/bmsisson/ 3 Our definition of binary tree is unusual but more convenient for our analysis. It is the same as full binary merging in [3]. 4 A binary reassembling in our sense mimicks what is called "agglomerative, or bottom-up, hierarchical clustering" in data mining. 5 To keep them apart, we reserve the words "node" and "branch" for the tree B, and the words "vertex" and "edge" for the graph G.

Scientific Reports, 2014

ArXiv, 2018

In this paper, we present an on-line fully dynamic algorithm for maintaining strongly connected component of a directed graph in a shared memory architecture. The edges and vertices are added or deleted concurrently by fixed number of threads. To the best of our knowledge, this is the first work to propose using linearizable concurrent directed graph and is build using both ordered and unordered list-based set. We provide an empirical comparison against sequential and coarse-grained. The results show our algorithm’s throughput is increased between 3 to 6x depending on different workload distributions and applications. We believe that there are huge applications in the on-line graph. Finally, we show how the algorithm can be extended to community detection in on-line graph.

Algorithms for Computational Biology

Dual graphs have been applied to model RNA secondary structures with pseudoknots, or intertwined base pairs. In previous works, a linear-time algorithm was introduced to partition dual graphs into maximally connected components called blocks and determine whether each block contains a pseudoknot or not. As pseudoknots can not be contained into two different blocks, this characterization allow us to efficiently isolate smaller RNA fragments and classify them as pseudoknotted or pseudoknot-free regions, while keeping these sub-structures intact. Moreover we have extended the partitioning algorithm by classifying a pseudoknot as either recursive or non-recursive in order to continue with our research in the development of a library of building blocks for RNA design by fragment assembly. In this paper we present a methodology that uses our previous results and classify pseudoknots into the classical H,K,L, and M types, based upon a novel representation of RNA secondary structures as dual directed graphs (i.e., digraphs). This classification would help the systematic analysis of RNA structure and prediction as for example the implementation of more accurate folding algorithms.

BMC systems biology, 2016

Identifying the gene regulatory networks governing the workings and identity of cells is one of the main challenges in understanding processes such as cellular differentiation, reprogramming or cancerogenesis. One particular challenge is to identify the main drivers and master regulatory genes that control such cell fate transitions. In this work, we reformulate this problem as the optimization problems of computing a Minimum Dominating Set and a Minimum Connected Dominating Set for directed graphs. Both MDS and MCDS are applied to the well-studied gene regulatory networks of the model organisms E. coli and S. cerevisiae and to a pluripotency network for mouse embryonic stem cells. The results show that MCDS can capture most of the known key player genes identified so far in the model organisms. Moreover, this method suggests an additional small set of transcription factors as novel key players for governing the cell-specific gene regulatory network which can also be investigated wi...

Sensors

Internet of Things (IoT) applications play a relevant role in today’s industry in sharing diagnostic data with off-site service teams, as well as in enabling reliable predictive maintenance systems. Several interventions scenarios, however, require the physical presence of a human operator: Augmented Reality (AR), together with a broad-band connection, represents a major opportunity to integrate diagnostic data with real-time in-situ acquisitions. Diagnostic information can be shared with remote specialists that are able to monitor and guide maintenance operations from a control room as if they were in place. Furthermore, integrating heterogeneous sensors with AR visualization displays could largely improve operators’ safety in complex and dangerous industrial plants. In this paper, we present a complete setup for a remote assistive maintenance intervention based on 5G networking and tested at a Vodafone Base Transceiver Station (BTS) within the Vodafone 5G Program. Technicians’ saf...

ACM Transactions on Information Systems, 2013

Although Web search engines still answer user queries with lists of ten blue links to webpages, people are increasingly issuing queries to accomplish their daily tasks (e.g., finding a recipe , booking a flight , reading online news , etc.). In this work, we propose a two-step methodology for discovering tasks that users try to perform through search engines. First, we identify user tasks from individual user sessions stored in search engine query logs. In our vision, a user task is a set of possibly noncontiguous queries (within a user search session), which refer to the same need. Second, we discover collective tasks by aggregating similar user tasks, possibly performed by distinct users. To discover user tasks, we propose query similarity functions based on unsupervised and supervised learning approaches. We present a set of query clustering methods that exploit these functions in order to detect user tasks. All the proposed solutions were evaluated on a manually-built ground tru...

Proceedings of the 27th ACM symposium on Parallelism in Algorithms and Architectures, 2015

This paper quantifies the impact of branches and branch mispredictions on the single-core performance for two classes of graph problems. Specifically, we consider classical algorithms for computing connected components and breadthfirst search (BFS). We show that branch mispredictions are costly and can reduce performance by as much as 30%-50%. This insight suggests that one should seek graph algorithms and implementations that avoid branches. As a proof-of-concept, we devise such implementations for both the classic top-down algorithm for BFS and the Shiloach-Vishkin algorithm for connected components. We evaluate these implementations on current x86 and ARMbased processors to show the efficacy of the approach. Our results suggest how both compiler writers and architects might exploit this insight to improve graph processing systems more broadly and create better systems for such problems.

Annals of Operations Research, 2016

We consider the Critical Node Problem: given an undirected graph and an integer number K, at most K nodes have to be deleted from the graph in order to minimize a connectivity measure in the residual graph. We combine the basic steps used in common greedy algorithms with some flavour of local search, in order to obtain simple hybrid heuristic algorithms. The obtained algorithms are shown to be effective, delivering improved performances (solution quality and speed) with respect to known greedy algorithms and other more sophisticated state of the art methods.

Frontiers in Neuroscience, 2022

Brain connectomics consists in the modeling of human brain as networks, mathematically represented as numerical connectivity matrices. However, this representation may result in difficult interpretation of the data. To overcome this limitation, graphical representation by connectograms is currently used via open-source tools, which, however, lack user-friendly interfaces and options to explore specific sub-networks. In this context, we developed SPIDER-NET (Software Package Ideal for Deriving Enhanced Representations of brain NETworks), an easy-to-use, flexible, and interactive tool for connectograms generation and sub-network exploration. This study aims to present SPIDER-NET and to test its potential impact on pilot cases. As a working example, structural connectivity (SC) was investigated with SPIDER-NET in a group of 17 healthy controls (HCs) and in two subjects with stroke injury (Case 1 and Case 2, both with a focal lesion affecting part of the right frontal lobe, insular cort...

Scientific Reports, 2017

We virtually dissect complex networks in order to understand their internal structure, just as doctors do with the bodies of animals. Our novel method classifies network links into four categories: bone, fat, cartilage, and muscle, based on network connectivity. We derive an efficient percolation strategy from this new viewpoint of network anatomy, which enables abrupt-like percolation transition through removal of a small amount of cartilage links, which play a crucial role in network connectivity. Furthermore, we find nontrivial scaling laws in the relationships between four types of links in each cluster and evaluate power exponents, which characterize network structures as seen in the real largescale network of trading business firms and in the Erdős-Rényi network. Finally, we observe changes in the transition point for random bond percolation process, demonstrating that the addition of muscle links enhances network robustness, while fat links are irrelevant. These findings aid in controlling the percolation transition for an arbitrary network. Different networks, such as human and business relationship networks, and power networks, are everywhere in our world 1-4. Most complex networks in social systems can be categorized as having scale-free and small-world properties 5, 6. Many methods quantifying such inhomogeneous networks have been proposed from various fields including biology, information science and physics 4, 6-9. It is important to understand how a network can be made robust under attack, including methods for intentional removal of nodes and links because such networks form the basis of the society and economy 10-14. Thus, it is necessary to determine what elements contribute to reinforcing network connectivity, and to find practical ways to enhance robustness of the system. Percolation theory has been studied in the fields of mathematics and physics to clarify macroscopic connectivity from a microscopic viewpoint 4, 15-20. Specifically, the percolation transition properties of complex networks have been attracting the attention of many scientists since the proposal of the scale-free network model 5. It has been reported that a scale-free network is fragile against targeted attacks, but robust against random failures 10. Furthermore, recent percolation models have been extended to explain a discontinuous percolation transition (DPT) 2, 18, 19, 21, 22. It has been suggested that a real power network carries the risk of massive blackouts due to cascading failures in a multi-layered network 2 , and discontinuity in the explosive percolation model has attracted great interest in recent years due to its simple yet diverse characteristics 23-25. Classification of nodes and links, such as community extraction, is also an important field of study, and comprehensive graphical expressions have become available for this application 26-30. In the theory of percolation transition for square lattices, there are studies classifying "backbone links" based on significant contribution to overall connectivity 31-33 , however, such classifications have not been yet introduced to percolation study in complex networks. In this study, we further generalize the anatomical concept of a "backbone" by introducing a novel "network anatomy", which virtually dissects any given complex network and classifies its links based on their contribution to network connectivity. In the Method section, all network links are classified into four categories: bone, fat, cartilage, and muscle links, as an analogy for the anatomy of animal bodies. In the Result 1 section, we show that a percolation strategy assembled from these link categories enables the abrupt-like transition in a large-scale real network, as well as artificial networks. Nontrivial scaling laws are observed among the four classified link types and scaling exponents that characterize a network are shown in the Result 2 section. In the Result 3 section, we observe shifts of the percolation transition point caused by doping fat and muscle links to clarify the functional

International Journal of Intelligent Systems, 2012

The ongoing exponential growth of online information sources has led to a need for reliable and efficient algorithms for text clustering.In this paper, we propose a novel text model called the relational text model that represents each sentence as a binary multirelation over a concept space C. Through usage of the smart indexing engine (SIE), a patented technology of the Belgian company i.Know, the concept space adopted by the text model can be constructed dynamically.This means that there is no need for an a priori knowledge base such as an ontology, which makes our approach context independent. The concepts resulting from SIE possess the property that frequency of concepts is a measure for relevance. We exploit this property with the development of the CR-algorithm. Our approach relies on the representation of a data set D as a multirelation, of which k-cuts can be taken. These cuts can be seen as sets of relevant patterns with respect to the topics that are described by documents. Analysis of dependencies between patterns allows to produce clusters, such that precision is sufficiently high. The best k-cut is the one that best approximates the estimated number of clusters to ensure recall. Experimental results on Dutch news fragments show that our approach outperforms both basic and advanced methods.

Physical Review E, 2021

Carreras, Dobson and colleagues have studied empirical data on the sizes of the blackouts in real grids and modeled them by computer simulations using the direct current approximation. They have found that the resulting blackout sizes are distributed as a power law and suggested that this is because the grids are driven to the self-organized critical state. In contrast, more recent studies found that the distribution of cascades is bimodal as in a first order phase transition, resulting in either a very small blackout or a very large blackout, engulfing a finite fraction of the system. Here we reconcile the two approaches and investigate how the distribution of the blackouts changes with model parameters, including the tolerance criteria and the dynamic rules of failure of the overloaded lines during the cascade. In addition, we study the same problem for the Motter and Lai model and find similar results, suggesting that the physical laws of flow on the network are not as important as network topology, overload conditions, and dynamic rules of failure.

Nature Communications, 2019

The adverse effect of climate change continues to expand, and the risks of flooding are increasing. Despite advances in network science and risk analysis, we lack a systematic mathematical framework for road network percolation under the disturbance of flooding. The difficulty is rooted in the unique three-dimensional nature of a flood, where altitude plays a critical role as the third dimension, and the current network-based framework is unsuitable for it. Here we develop a failure model to study the effect of floods on road networks; the result covers 90.6% of road closures and 94.1% of flooded streets resulting from Hurricane Harvey. We study the effects of floods on road networks in China and the United States, showing a discontinuous phase transition, indicating that a small local disturbance may lead to a large-scale systematic malfunction of the entire road network at a critical point. Our integrated approach opens avenues for understanding the resilience of critical infrastructure networks against floods.

Mathematics

Electoral systems are modified by individuals who have incentives to bias the rules for their political advantage (i.e., gerrymandering). To prevent gerrymandering, legislative institutions can rely on mathematical tools to guarantee democratic fairness and territorial contiguity. These tools have been successfully used in the past; however, there is a need to accommodate additional meanings of the term fairness within the electoral systems of modern democracies. In this paper, we present an optimization framework that considers multiple criteria for drawing districts and assigning the number of representatives. Besides some typical districting criteria (malapportionment and contiguity), we introduce novel criteria for ensuring territorial equilibrium and incentives for candidates to deploy their representation efforts fairly during their campaign and period in office. We test the method, which we denote as Multi-criteria Pen, in a recent and a forthcoming reform of the Chilean elec...

Optimization, 2018

The MINIMUM CONNECTIVITY INFERENCE (MCI) problem represents an N P-hard generalization of the well-known minimum spanning tree problem and has been studied in different fields of research independently. Let an undirected complete graph and finitely many subsets (clusters) of its vertex set be given. Then, the MCI problem is to find a minimal subset of edges so that every cluster is connected with respect to this minimal subset. Whereas, in general, existing approaches can only be applied to find approximate solutions or optimal edge sets of rather small instances, concepts to optimally cope with more meaningful problem sizes have not been proposed yet in literature. For this reason, we present a new mixed integer linear programming formulation for the MCI problem, and introduce new instance reduction methods that can be applied to downsize the complexity of a given instance prior to the optimization. Based on theoretical and computational results both contributions are shown to be beneficial for solving larger instances.

Studies in Computational Intelligence, 2016

While a visual unconstrained tree structure planar layout design is easy to implement, a visualization of a tree with constraints on node ranks and their ordering within ranks leads to a difficult combinatorial problem. A genealogical graph, such as family tree, can be taken as an example of such a case. Classical ancestor trees, descendant trees, Hourglass charts, and their visual variants such as node-link diagrams or fan charts are suitable for assessment of peoples relationships when one is focused on a particular person and his/her direct ancestors and descendants. Such tree-based representations miss a broader context of relationships and do not allow the quick assessment of several interlinked families together. We propose a new undirected tree-driven layout technique for layered multitree graph visualizations producing constraints on node layers and ordering of groups of nodes within layers. The computed constraints can be mapped, at least partially, into the DOT language property directives used by the Graphviz toolbox. We demonstrate achievements on several datasets containing up to 39000 people.

ACM Computing Surveys, 1977

This survey includes an introduction to the concepts of problem complexity, analysis of algorithms to find bounds on complexity, average-case behavior, and approximation algomthms The major techmques used m analysis of algorithms are reviewed and examples of the use of these methods are presented. A brief explanation of the problem classes P and NP, as well as the class of NP-complete problems, is also presented.

Lecture Notes in Computer Science, 2010

Facts are multidimensional concepts of primary interests for knowledge workers because they are related to events occurring dynamically in an organization. Normally, these concepts are modeled in operational data sources as tables. Thus, one of the main steps in conceptual design of a data warehouse is to detect the tables that model facts. However, this task may require a high level of expertise in the application domain, and is often tedious and time-consuming for designers. To overcome these problems, a comprehensive model-driven approach is presented in this paper to support designers in: (1) obtaining a CWM model of business-related relational tables, (2) determining which elements of this model can be considered as facts, and (3) deriving their counterparts in a multidimensional schema. Several heuristics-based on structural information derived from data sources-have been defined to this end and included in a set of Query/View/Transformation model transformations.

Land, 2017

Many developing countries have witnessed the urgent need of accelerating cadastral surveying processes. Previous studies found that large portions of cadastral boundaries coincide with visible physical objects, namely roads, fences, and building walls. This research explores the application of airborne laser scanning (ALS) techniques on cadastral surveys. A semi-automated workflow is developed to extract cadastral boundaries from an ALS point clouds. Firstly, a two-phased workflow was developed that focused on extracting digital representations of physical objects. In the automated extraction phase, after classifying points into semantic components, the outline of planar objects such as building roofs and road surfaces were generated by an α-shape algorithm, whilst the centerlines delineatiation approach was fitted into the lineate object-a fence. Afterwards, the extracted vector lines were edited and refined during the post-refinement phase. Secondly, we quantitatively evaluated the workflow performance by comparing results against an exiting cadastral map as reference. It was found that the workflow achieved promising results: around 80% completeness and 60% correctness on average, although the spatial accuracy is still modest. It is argued that the semi-automated extraction workflow could effectively speed up cadastral surveying, with both human resources and equipment costs being reduced.

Journal of Graph Theory

Let G be a graph on n vertices. For i ∈ {0, 1} and a connected graph G, a spanning forest F of G is called an i-perfect forest if every tree in F is an induced subgraph of G and exactly i vertices of F have even degree (including zero). A i-perfect forest of G is proper if it has no vertices of degree zero. Scott (2001) showed that every connected graph with even number of vertices contains a (proper) 0-perfect forest. We prove that one can find a 0-perfect forest with minimum number of edges in polynomial time, but it is NP-hard to obtain a 0-perfect forest with maximum number of edges. We also prove that for a prescribed edge e of G, it is NP-hard to obtain a 0-perfect forest containing e, but we can find a 0-perfect forest not containing e in polynomial time. It is easy to see that every graph with odd number of vertices has a 1-perfect forest. It is not the case for proper 1-perfect forests. We give a characterization of when a connected graph has a proper 1-perfect forest.

PLoS computational biology, 2015

All biological evolution takes place in a space of possible genotypes and their phenotypes. The structure of this space defines the evolutionary potential and limitations of an evolving system. Metabolism is one of the most ancient and fundamental evolving systems, sustaining life by extracting energy from extracellular nutrients. Here we study metabolism&#39;s potential for innovation by analyzing an exhaustive genotype-phenotype map for a space of 1015 metabolisms that encodes all possible subsets of 51 reactions in central carbon metabolism. Using flux balance analysis, we predict the viability of these metabolisms on 10 different carbon sources which give rise to 1024 potential metabolic phenotypes. Although viable metabolisms with any one phenotype comprise a tiny fraction of genotype space, their absolute numbers exceed 109 for some phenotypes. Metabolisms with any one phenotype typically form a single network of genotypes that extends far or all the way through metabolic geno...

Proceedings of the 2021 International Conference on Management of Data, 2021

Supervised and Unsupervised ML algorithms are widely used over graphs. They use the structural properties of the data to deliver effective results. It is known that the same information can be represented under various graph structures. Thus, these algorithms may be effective on some structural variations of the data and ineffective on others. One would like to have an algorithm that is effective and generalizes to all structural variations of a data graph. We define the concept of structural generalizability for algorithms over graphs. We focus on the problem of similarity search, which is a popular task and the building block of many ML algorithms on graphs, and propose a structurally generalizable similarity search algorithm. As this algorithm may require users to specify features in a rather complex language, we modify this algorithm so that it requires only simple guidance from the user. Our extensive empirical study show that our algorithms are structurally generalizable while being efficient and more effective than current algorithms. CCS CONCEPTS • Information systems → Graph-based database models; Data mining.

Foundations of Computational Mathematics, 2016

We give deterministic polynomial-time algorithms that, given an order, compute the primitive idempotents and determine a set of generators for the group of roots of unity in the order. Also, we show that the discrete logarithm problem in the group of roots of unity can be solved in polynomial time. As an auxiliary result, we solve the discrete logarithm problem for certain unit groups in finite rings. Our techniques, which are taken from commutative algebra, may have further potential in the context of cryptology and computer algebra.

Pesquisa Operacional, 2017

In this work, the presence of cut nodes in a network is exploited to propose a competitive method for the multi-terminal maximum flow problem. The main idea of the method is based on the relation between cut-trees and cut nodes, which is observed in the context of sensitivity analysis on the variation of edges capacities. Computational experiments were conducted with the proposed algorithm, whose results were compared with the ones of Gusfield, for randomly generated and well-known instances of the literature. The numerical results demonstrate the potential of the method for some classes of instances. Moreover, the proposed method was adapted for the single maximum flow problem, but failed to improve existing running times for the very same classes of instances.

Algorithmica, 2021

For a clustered graph, i.e, a graph whose vertex set is recursively partitioned into clusters, the C-Planarity Testing problem asks whether it is possible to find a planar embedding of the graph and a representation of each cluster as a region homeomorphic to a closed disk such that (1) the subgraph induced by each cluster is drawn in the interior of the corresponding disk, (2) each edge intersects any disk at most once, and (3) the nesting between clusters is reflected by the representation, i.e., child clusters are properly contained in their parent cluster. The computational complexity of this problem, whose study has been central to the theory of graph visualization since its introduction in 1995 [Feng, Cohen, and Eades, Planarity for clustered graphs, ESA’95], has only been recently settled [Fulek and Tóth, Atomic Embeddability, Clustered Planarity, and Thickenability, to appear at SODA’20]. Before such a breakthrough, the complexity question was still unsolved even when the gr...

Operations Research, 2022

Authors are encouraged to submit new papers to INFORMS journals by means of a style file template, which includes the journal title. However, use of a template does not certify that the paper has been accepted for publication in the named journal. INFORMS journal templates are for the exclusive purpose of submitting to an INFORMS journal and should not be used to distribute the papers in print or online or to submit the papers to another publication.

AKCE International Journal of Graphs and Combinatorics, 2020

A vertex (respectively, edge) cycle stochastic function of a graph G is a labeling of vertices (respectively, edges) by a non-negative real valued function f V : such that for every cycle of G, the sum of labels of its vertices (respectively, edges) is 1. The graphs where we can define such a function are called vertex cycle stochastic graphs (respectively, edge cycle stochastic graphs). In this paper, we provide a structure theorem for biconnected cycle stochastic graphs, which is extended to characterize edge cycle stochastic graphs. We also find a minimal forbidden graph characterization for biconnected vertex cycle stochastic graphs and its description for vertex cycle stochastic graphs.

Applied Network Science

Graph sampling methods have been used to reduce the size and complexity of big complex networks for graph mining and visualization. However, existing graph sampling methods often fail to preserve the connectivity and important structures of the original graph. This paper introduces a new divide and conquer approach to spectral graph sampling based on graph connectivity, called the BC Tree (i.e., decomposition of a connected graph into biconnected components) and spectral sparsification. Specifically, we present two methods, spectral vertex sampling$$BC\_SV$$BC_SVand spectral edge sampling$$BC\_SS$$BC_SSby computing effective resistance values of vertices and edges for each connected component. Furthermore, we present$$DBC\_SS$$DBC_SSand$$DBC\_GD$$DBC_GD, graph connectivity-based distributed algorithms for spectral sparsification and graph drawing respectively, aiming to further improve the runtime efficiency of spectral sparsification and graph drawing by integrating connectivity-ba...

ACM Journal of Experimental Algorithms, 2018

Betweenness Centrality (BC) is steadily growing in popularity as a metrics of the influence of a vertex in a graph. The BC score of a vertex is proportional to the number of all-pairs-shortestpaths passing through it. However, complete and exact BC computation for a large-scale graph is an extraordinary challenge that requires high performance computing techniques to provide results in a reasonable amount of time. Our approach combines bi-dimensional (2-D) decomposition of the graph and multi-level parallelism together with a suitable data-thread mapping that overcomes most of the difficulties caused by the irregularity of the computation on GPUs. Furthermore, we propose novel heuristics which exploit the topology information of the graph in order to reduce time and space requirements of BC computation. Experimental results on synthetic and real-world graphs show that the proposed techniques allow the BC computation of graphs which are too large to fit in the memory of a single computational node along with a significant reduction of the computing time.