An effective branch-and-bound algorithm for the maximum s-bundle problem

•We exploit the properties of the maximum s-bundle problem.•A branch-and-bound algorithm is proposed for the maximum s-bundle problem.•We study novel multi-branching techniques.•Numerical results show the benefit of the new algorithm compared to existing ones. An s-bundle (where s is a positive inte...

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Bibliographic Details
Published in:European journal of operational research Vol. 297; no. 1; pp. 27 - 39
Main Authors: Zhou, Yi, Lin, Weibo, Hao, Jin-Kao, Xiao, Mingyu, Jin, Yan
Format: Journal Article
Language:English
Published: Elsevier B.V 16.02.2022
Elsevier
Subjects:
[formula omitted]-Bundle
Branch and bound
Clique relaxation
Combinatorial optimization
Computer Science
Graph theory
Clique relaxation
Graph theory
Branch and bound
Combinatorial optimization
s-Bundle
ISSN:0377-2217, 1872-6860
Online Access:Get full text
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Summary:•We exploit the properties of the maximum s-bundle problem.•A branch-and-bound algorithm is proposed for the maximum s-bundle problem.•We study novel multi-branching techniques.•Numerical results show the benefit of the new algorithm compared to existing ones. An s-bundle (where s is a positive integer) is a connected graph, the vertex connectivity of which is at least n−s, where n is the number of vertices in the graph. As a relaxation of the classical clique model, the s-bundle is relevant for representing cohesive groups with an emphasis on the connectivity of members; thus, it is of great practical importance. In this work, we investigate the fundamental problem of finding the maximum s-bundle from a given graph and present an effective branch-and-bound algorithm for solving this NP-hard problem. The proposed algorithm is distinguished owing to its new multi-branching rules, graph coloring-based bounding technique, and reduction rules using structural information. The experiments indicate that the algorithm outperforms the best-known approaches on a wide range of well-known benchmark graphs for different s values. In particular, compared with the popular Russian Doll Search algorithm, the proposed algorithm almost doubles the success rate of solving large social networks in an hour when s=5.
ISSN:0377-2217
1872-6860
DOI:10.1016/j.ejor.2021.05.001