A Lagrangian Bound on the Clique Number and an Exact Algorithm for the Maximum Edge Weight Clique Problem

• Type: Article in International Scientific Journal
• Date: 2020

Authors

Hosseinian, S (Author) Other; Dalila B.M.M. Fontes (Author) FEP; Butenko, S (Author) Other

Journal

Title: INFORMS Journal on Computing

Vol. 32 No. 3

Pages: 747-762

ISSN: 1091-9856

Publisher: Institute for Operations Research and the Management Sciences

Indexing

ISI Web of Knowledge - 6 Citations

Scopus

Other information

Authenticus ID: P-00R-R6Z

DOI: 10.1287/ijoc.2019.0898

Abstract (EN): 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.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 16