Journal
INFORMS JOURNAL ON COMPUTING
Volume 32, Issue 3, Pages 747-762Publisher
INFORMS
DOI: 10.1287/ijoc.2019.0898
Keywords
graph theory; analytic upper bound on the clique number; maximum edge weight clique problem
Categories
Funding
- National Science Foundation [CMMI-1538493]
- Office of Naval Research [N00014-13-1-0635]
- Portuguese Foundation for Science and Technology [POCI-01-0145-FEDER-031821]
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This paper explores the connections between the classical maximum clique problem and its edge-weighted generalization, the maximum edge weight clique (MEWC) problem. As a result, a new analytic upper bound on the clique number of a graph is obtained and an exact algorithm for solving the MEWC problem is developed. The bound on the clique number is derived using a Lagrangian relaxation of an integer (linear) programming formulation of the MEWC problem. Furthermore, coloring-based bounds on the clique number are used in a novel upper-bounding scheme for the MEWC problem. This scheme is employed within a combinatorial branch-and-bound framework, yielding an exact algorithm for the MEWC problem. Results of computational experiments demonstrate a superior performance of the proposed algorithm compared with existing approaches.
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