A new algorithm to compute vertex cutsets in a graph

IAES International Journal of Artificial Intelligence (IJ-AI), 2020

Reliability evaluation is an important research field for a complex network. The most popular methods for such evaluation often use Minimal Cuts (MC) or Minimal paths (MP). Nonetheless, few algorithms address the issue of the enumeration of all minimal cut sets from the source node s to the terminal node t when only the nodes of the network are subject to random failures. This paper presents an effective algorithm which enumerates all minimal node cuts sets of a network. The proposed algorithm runs in two steps: The first one is used to generate a subset of paths, called necessary minimal paths, instead of all minimal paths. Whereas, the second step stands to build all minimal cutsets from the necessary minimal paths.

2000

: We provide an algorithm for enumerating near-minimum weight s-t cuts in directed and undirected graphs, with applications to network interdiction and network reliability. "Near-minimum" means within a factor of l+epilson of the minimum for some epilson > 0. The algorithm is based on recursive inclusion and exclusion of edges in locally minimum-weight cuts identified with a maximum flow algorithm. We prove a polynomial-time complexity result when epilson = 0, and for epilson > 0 we demonstrate good empirical efficiency. The algorithm is programmed in Java, run on a 733 MHz Pentium III computer with 128 megabytes of memory, and tested on a number of graphs. For example, all 274,550 near-minimum cuts within 10% of the minimum weight can be obtained in 74 seconds for a 627 vertex 2,450 edge unweighted graph. All 20,806 near-minimum cuts within 20% of minimum can be enumerated in 61 seconds on the same graph with weights being uniformly distributed integers in the range...

AASRI Procedia, 2013

Network reliability analysis problem is the center of many scientific productions. It consists of evaluating the all-terminal reliability of networks. Two classes have emerged; exact and approximate methods. The aim of this paper is to present an efficient exact method for enumerating minimal cuts (MCS) of R-networks. The algorithm proceeds by determining minimal paths set (MPS) and from which minimal cuts are generated by managing binary decision diagrams. The manipulation process consists of a series of transformations, reductions and filtering operations. The approach succeeds in the reduction of computation time and memory space and was applied for evaluating the reliability of a national radio communication network.

2020

When multiple outages occur in rapid succession, it is important to know quickly if the power transfer capability of different interconnections (or cut-sets) of the power network are limited. The algorithm developed in this paper identifies such limited cut-sets very fast, thereby enhancing the real-time situational awareness of power system operators. The significance of the proposed approach is described using the IEEE 39-bus test system, while its computational benefits are demonstrated using relatively large test-cases containing thousands of buses. The results indicate that the proposed network analysis can estimate the impact of an outage on any cut-set of the system and screen out the cut-set that gets saturated by the largest margin, very quickly.

Zenodo (CERN European Organization for Nuclear Research), 2022

Let G be an undirected graph, and s, t distinguished vertices of G. A minimal st-separator is an inclusion-wise minimal vertex-set whose removal places s and t in distinct connected components. We consider the problem of listing the minimal st-separators of G in ascending order of their weight (or cardinality). We present such a ranked-enumeration algorithm for P k-free graphs with maximum degree d, that has a delay of poly(|V(G)|, |E(G)|)3 4kd 3 , making it the first fixed-parameter-delay enumeration algorithm for this problem. In the process, we provide new characterizations of minimal st-separators that are of independent interest, and describe the obstacles for obtaining a polynomial delay algorithm.

Computational Optimization and Applications, 2012

The max-cut problem asks for partitioning the nodes V of a graph G = (V, E) into two sets (one of which might be empty), such that the sum of weights of edges joining nodes in different partitions is maximum. Whereas for general instances the max-cut problem is NPhard, it is polynomially solvable for certain classes of graphs. For planar graphs, there exist several polynomial-time methods determining maximum cuts for arbitrary choice of edge weights. Typically, the problem is solved by computing a minimum-weight perfect matching in some associated graph. The most efficient known algorithms are those of Shih et al. [45] and that of Berman et al. [9]. The running time of the former can be bounded by O(|V | 3 2 log |V |). The latter algorithm is more generally for determining T-joins in graphs. Although it has a slightly larger bound on the running time of O([V | 3 2 (log |V |) 3 2)α(|V |), where α(|V |) is the inverse Ackermann function, it can solve large instances in practice. In this work, we present a new and simple algorithm for determining maximum cuts for arbitrary weighted planar graphs. Its running time is bounded by O(|V | 3 2 log |V |), similar to the bound achieved by [45]. It can easily determine maximum cuts in huge random as well as real-world graphs with up to 10 6 nodes. We present experimental results for our method using two different matching implementations. We furthermore compare our approach with those of [45] and [9]. It turns out that our algorithm is considerably faster in practice than [45]. Moreover, it yields a much smaller associated graph. Its expanded graph size is comparable to that of [9]. However, whereas the procedure of generating the expanded graph in [9] is very involved (thus needs a sophisticated implementation), implementing our approach is an easy and straightforward task.

In this paper we propose an algorithm for obtaining all minimal cut sets for a given two-terminal network. The algorithm works on undirected networks without matter whether they are coherent or not. The difference between this algorithm and the other proposed algorithms is in the fact that there are not received candidates for minimal cut set that are not minimal cut sets. A large part of the paper proves the correctness of the algorithm and analyzes its complexity.

Evaluating network reliability is an important topic in the planning, designing and control of network systems. Modifications are common for network expansion or reinforcement evaluation and planning. A modified network is an updated network after inserting a branch string (a special path) between two nodes in the original network. The problem of searching all minimal cuts (MCs) in a modified network is discussed and solved in this study. The proposed algorithm is easier to understand and implement than the existing known related algorithms. The accuracy of the proposed algorithm will be validated. The computational complexity of the proposed algorithm is analyzed and compared with the existing best-known methods. One benchmark example is illustrated to show how to find all MCs in a modified network using the information of all the MCs in the corresponding original network.

Computational Optimization and Applications, 2004

In this paper, a sequential algorithm is presented to find all cut-vertices on trapezoid graphs. To every trapezoid graph G there is a corresponding trapezoid representation. If all the 4n corner points of n trapezoids, in a trapezoid representation of a trapezoid graph G with n vertices, are given, then the proposed sequential algorithm runs in O(n) time. Parallel implementation of this algorithm can be done in O(log n) time using O(n/ log n) processors on an EREW PRAM model.

Journal of Independent Studies and Research - Computing, 2015

Graph Partitioning is one of the favorite research topics among researchers since the 70s. It attracts a diverse group of researchers from various fields such as engineering, science and mathematics. In the last decade, the graphs have increased in size to billions of vertices. Despite the fact that storage devices have become cheaper, processing these huge spanning graphs is not possible for a single machine. This call for the need of partitioning the graph so a group of machines can perform various parallel calculations on them which would save time and produce quick results. The research problem is that the ratio of boundary vertices to interior vertices increases with the increase in number of partitions for existing partitioning techniques available. To address this issue, the random edge selection method of Graph Lab algorithm was replaced with four suggested edge sorting techniques. The results were compared with the random edge selection method of Graph Lab using various performance parameters.