Approximation Algorithms for Min-k-Overlap Problems Using the Principal Lattice of Partitions Approach

Narayanan, Hariharan; Roy, Subir Kumar; Patkar, Sachin B.

doi:10.1006/jagm.1996.0047

Cited by 19 publications

(4 citation statements)

References 11 publications

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“…This problem is similar to the MINIMUM k-VERTEX SHARING [21], where the objective is to minimize the number of nodes deleted to achieve a k-way partition. Here we are considering the complementary problem, where we know the number of vertices to be deleted and we try to maximize the number of components formed and implicitly limit the sizes of the components.…”

Section: Problem Definitionmentioning

confidence: 99%

Detecting critical nodes in sparse graphs

Arulselvan

Commander

Elefteriadou

2009

Computers & Operations Research

302

252

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ABSTRACT. Identifying critical nodes in a graph is important to understand the structural characteristics and the connectivity properties of the network. In this paper, we focus on detecting critical nodes, or nodes whose deletion results in the minimum pair-wise connectivity among the remaining nodes. This problem, known as the CRITICAL NODE PROBLEM has applications in several fields including biomedicine, telecommunications, and military strategic planning. We show that the recognition version of the problem is N P -complete and derive a mathematical formulation based on integer linear programming. In addition, we propose a heuristic for the problem which exploits the combinatorial structure of the graph. The heuristic is then enhanced by the application of a local improvement method. A computational study is presented in which we apply the integer programming formulation and the heuristic to real and randomly generated data sets. For all instances tested, the heuristic is able to efficiently provide optimal solutions in a fraction of the time required by a commercial software package.

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Section: Problem Definitionmentioning

confidence: 99%

Detecting critical nodes in sparse graphs

Arulselvan

Commander

Elefteriadou

2009

Computers & Operations Research

302

252

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“…With another method, when a hyperedge straddles p different subsets, the weight of that hyperedge is counted p -1 times. These cost functions are represented by cost 1 )-approximation algorithm have previously been obtained, respectively [66] (where d max is the maximum degree of a hyperedge).…”

Section: Application To Different Cost Functions In Hypergraphsmentioning

confidence: 99%

Algorithms for the minimum partitioning problems in graphs

Nagamochi

2007

Electron Comm Jpn Pt III

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SUMMARYIn this paper, the author explains the recent evolution of algorithms for minimum partitioning problems in graphs. When the set of vertices of a graph having nonnegative weights for edges is divided into k subsets, the set of edges for which both endpoints are contained in different subsets is called a k-way cut or k-cut. The problem of obtaining the k-way cut that minimizes the sum of the weights is an important research topic that appears in many practical applications such as VLSI design. In this paper, the author introduces recent results including cases in which sets of terminals or sets of terminal pairs that are to be separated are further specified in this problem and cases in which the objects to be partitioned are extended from graphs to hypergraphs or submodular set functions.

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“…This article considers the critical infrastructure detection problem as follows: Given a telecommunication network with V facilities as nodes and an integer K, the objective is to find a set of K facilities (critical nodes) in this network whose failure results in the maximum network disruption and this problem can be considered as a special case of Minimum-Koverlap problem (Narayanan, Roy, & Patkar, 1996). With the notation of y i where y i is 1 if facility i is removed from the optimal infrastructure and 0 otherwise.…”

Section: Complex Network and Critical Infrastructure Detectionmentioning

confidence: 99%

Critical Infrastructure Management for Telecommunication Networks

Wang

Alidaee

Wang

et al. 2014

International Journal of Knowledge and Systems Science

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Telecommunication network infrastructures both stationary and ad hoc, play an important role in maintaining the stability of society worldwide. The protection of these critical infrastructures and their supporting structures become highly challenged due to its complexity. The understanding of interdependency of these infrastructures is the essential step to protect these infrastructures from destruction and attacks. This paper presents a critical infrastructure detection model to discover the interdependency based on the theories from social networks and new telecommunication pathways while this study transforms social theory into computational constructions. The procedure and solution of protecting critical infrastructures are discussed and computational results from the proposed model are presented.

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Approximation Algorithms for Min-k-Overlap Problems Using the Principal Lattice of Partitions Approach

Cited by 19 publications

References 11 publications

Detecting critical nodes in sparse graphs

Detecting critical nodes in sparse graphs

Algorithms for the minimum partitioning problems in graphs

Critical Infrastructure Management for Telecommunication Networks

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