Upper bounds and heuristics for the 2-club problem

Given an undirected graph G = ( V, E), a k-club is a subset of V that induces a subgraph of diameter at most k. The k-club problem is that of finding the maximum cardinality k-club in G. In this paper we present valid inequalities for the 2-club polytope and derive conditions for them to define face...

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Bibliographic Details
Published in:European journal of operational research Vol. 210; no. 3; pp. 489 - 494
Main Authors: Carvalho, Filipa D., Almeida, M. Teresa
Format: Journal Article
Language:English
Published: Amsterdam Elsevier B.V 01.05.2011
Elsevier
Elsevier Sequoia S.A
Series:European Journal of Operational Research
Subjects:
Applied sciences
Combinatorial optimization
Combinatorial optimization Integer programming k-club problem Heuristics
Computer science; control theory; systems
Cutting
Density
Exact sciences and technology
Flows in networks. Combinatorial problems
Graph theory
Graphs
Heuristic
Heuristics
Inequalities
Information retrieval. Graph
Integer programming
k-club problem
Linear programming
Mathematical models
Mathematical programming
Operational research
Operational research and scientific management
Operational research. Management science
Optimization
Optimization algorithms
Studies
Theoretical computing
Upper bounds
Integer programming
k-club problem
Combinatorial optimization
Heuristics
Polytope
Linear programming
Cutting plane method
Upper bound
Cardinal number
Optimal solution
Heuristic method
Subgraph
Relaxation method
Diameter
Non directed graph
ISSN:0377-2217, 1872-6860
Online Access:Get full text
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Summary:Given an undirected graph G = ( V, E), a k-club is a subset of V that induces a subgraph of diameter at most k. The k-club problem is that of finding the maximum cardinality k-club in G. In this paper we present valid inequalities for the 2-club polytope and derive conditions for them to define facets. These inequalities are the basis of a strengthened formulation for the 2-club problem and a cutting plane algorithm. The LP relaxation of the strengthened formulation is used to compute upper bounds on the problem’s optimum and to guide the generation of near-optimal solutions. Numerical experiments indicate that this approach is quite effective in terms of solution quality and speed, especially for low density graphs.
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ISSN:0377-2217
1872-6860
DOI:10.1016/j.ejor.2010.11.023