Open Access
A continuous based heuristic for the maximum clique problem.
Luana E. Gibbons,Donald W. Hearn,Panos M. Pardalos +2 more
- pp 103-124
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TLDR
A deterministic heuristic based on a continuous quadratic nonconvex formulation of the maximum clique problem that avoids the need for the calibration of parameters while maintaining computational competitiveness to greedy randomized search procedures which require such calibration.Abstract:
We develop a deterministic heuristic based on a continuous quadratic nonconvex formulation of the maximum clique problem. The developed heuristic avoids the need for the calibration of parameters while maintaining computational competitiveness to greedy randomized search procedures which require such calibration. Furthermore it demonstrates the potential for using continuous approaches to model discrete problems. Experimental results on test problems.read more
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Book ChapterDOI
The maximum clique problem
TL;DR: A survey of results concerning algorithms, complexity, and applications of the maximum clique problem is presented and enumerative and exact algorithms, heuristics, and a variety of other proposed methods are discussed.
Journal ArticleDOI
Matching hierarchical structures using association graphs
TL;DR: It is proved that, in the new formulation, there is a one-to-one correspondence between maximal cliques and maximal subtree isomorphisms, which allows the tree matching problem to be cast as an indefinite quadratic program using the Motzkin-Straus theorem.
Journal ArticleDOI
Reactive Local Search for the Maximum Clique Problem1
R. Battiti,M. Protasi +1 more
TL;DR: In this paper, a new Reactive Local Search (RLS) algorithm is proposed for the solution of the maximum-clique problem, which is based on local search complemented by a feedback (history-sensitive) scheme to determine the amount of diversification.
Book ChapterDOI
Matching Hierarchical Structures Using Association Graphs
TL;DR: A solution to the problem of matching two trees, by constructing the association graph using the graph-theoretic concept of connectivity, and proving that in the new formulation there is a one-to-one correspondence between maximal cliques and maximal subtree isomorphisms.
Journal ArticleDOI
Replicator Equations, Maximal Cliques, and Graph Isomorphism
TL;DR: A new energy-minimization framework for the graph isomorphism problem that is based on an equivalent maximum clique formulation that ensures a clear one-to-one correspondence exists between the solutions of the quadratic program and those in the original, combinatorial problem.