Maximum (Weight) Clique Problem Solving

A clique of a graph is a subset of the vertices that are all pairwise adjacent. Clique is an important graph-theoretic concept, and is often used to represent dense clusters. The maximum clique problem (MaxClq) is a long-standing problem in graph theory, for which the task is to find a clique with the maximum number of vertices in the given graph. An important generalization of MaxClq is the maximum weight clique problem (MaxWClq), in which each vertex is associated with a positive integer, and the goal is to find a clique with the largest weight. MWCPhas valuable applications in many fields

Solvers for MaxWClq

FastWClq works in a construct-and-reduce way, which interleaves between clique construction and graph reduction. FastWClq works particularly well for large sparse graphs.
---Reference: Shaowei Cai, Jinkun Lin: Fast Solving Maximum Weight Clique Problem in Massive Graphs. In Proc. of IJCAI 2016: 568-574
LSCC is a local search solver for MaxWClq and is good at dense graphs. LSCC+BMS is an improved version of LSCC for large sparse graphs. For more information, please visit pages of Yiyuan Wang
---Reference: Yiyuan Wang, Shaowei Cai, Minghao Yin: Two Efficient Local Search Algorithms for Maximum Weight Clique Problem. AAAI 2016: 805-811

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