A Lagrangian Bound on the Clique Number and an Exact Algorithm for the Maximum Edge Weight Clique Problem-Reference-Cited by-同舟云学术

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

Published:2020-07 Issue:3 Volume:32 Page:747-762
ISSN:1091-9856
Container-title:INFORMS Journal on Computing
language:en
Short-container-title:INFORMS Journal on Computing

Author:

Hosseinian Seyedmohammadhossein¹^ORCID,Fontes Dalila B. M. M.²^ORCID,Butenko Sergiy¹^ORCID

Affiliation:

1. Industrial & Systems Engineering, Texas A&M University, College Station, Texas 77843;

2. Institute for Systems and Computer Engineering, Technology and Science and Faculdade de Economia, Universidade do Porto, 4200-465 Porto, Portugal

Abstract

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.

Publisher

Institute for Operations Research and the Management Sciences (INFORMS)

Subject

General Engineering

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