A Semi-exact Algorithm for Quickly Computing A Maximum Weight Clique in Large Sparse Graphs

This paper explores techniques to quickly solve the maximum weight clique problem (MWCP) in very large scale sparse graphs. Due to their size, and the hardness of MWCP, it is infeasible to solve many of these graphs with exact algorithms. Although recent heuristic algorithms make progress in solving...

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Bibliographic Details
Published inThe Journal of artificial intelligence research Vol. 72; pp. 39 - 67
Main Authors Cai, Shaowei, Lin, Jinkun, Wang, Yiyuan, Strash, Darren
Format Journal Article
LanguageEnglish
Published San Francisco AI Access Foundation 01.01.2021
Subjects
Algorithms
Apexes
Artificial intelligence
Data reduction
Graphs
Heuristic methods
Run time (computers)
Very large scale
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Summary:This paper explores techniques to quickly solve the maximum weight clique problem (MWCP) in very large scale sparse graphs. Due to their size, and the hardness of MWCP, it is infeasible to solve many of these graphs with exact algorithms. Although recent heuristic algorithms make progress in solving MWCP in large graphs, they still need considerable time to get a high-quality solution. In this work, we focus on solving MWCP for large sparse graphs within a short time limit. We propose a new method for MWCP which interleaves clique finding with data reduction rules. We propose novel ideas to make this process efficient, and develop an algorithm called FastWClq. Experiments on a broad range of large sparse graphs show that FastWClq finds better solutions than state-of-the-art algorithms while the running time of FastWClq is much shorter than the competitors for most instances. Further, FastWClq proves the optimality of its solutions for roughly half of the graphs, all with at least 105 vertices, with an average time of 21 seconds.
ISSN:1076-9757
1076-9757
1943-5037
DOI:10.1613/jair.1.12327