An effective local search for the maximum clique problem

2005 ◽  
Vol 95 (5) ◽  
pp. 503-511 ◽  
Author(s):  
Kengo Katayama ◽  
Akihiro Hamamoto ◽  
Hiroyuki Narihisa
Keyword(s):  
Local Search ◽  
Maximum Clique ◽  
Maximum Clique Problem ◽  
Clique Problem

Cooperating local search for the maximum clique problem

2010 ◽  
Vol 17 (2) ◽  
pp. 181-199 ◽  
Author(s):  
Wayne Pullan ◽  
Franco Mascia ◽  
Mauro Brunato
Keyword(s):  
Local Search ◽  
Maximum Clique ◽  
Maximum Clique Problem ◽  
Clique Problem

scholarly journals Dynamic Local Search for the Maximum Clique Problem

2006 ◽  
Vol 25 ◽  
pp. 159-185 ◽  
Author(s):  
W. Pullan ◽  
H. H. Hoos
Keyword(s):  
Local Search ◽  
Search Algorithm ◽  
Maximum Clique ◽  
Maximum Clique Problem ◽  
Stochastic Local Search ◽  
Performance Improvements ◽  
Benchmark Instances ◽  
Iterative Improvement ◽  
Selection Of ◽  
Clique Problem

In this paper, we introduce DLS-MC, a new stochastic local search algorithm for the maximum clique problem. DLS-MC alternates between phases of iterative improvement, during which suitable vertices are added to the current clique, and plateau search, during which vertices of the current clique are swapped with vertices not contained in the current clique. The selection of vertices is solely based on vertex penalties that are dynamically adjusted during the search, and a perturbation mechanism is used to overcome search stagnation. The behaviour of DLS-MC is controlled by a single parameter, penalty delay, which controls the frequency at which vertex penalties are reduced. We show empirically that DLS-MC achieves substantial performance improvements over state-of-the-art algorithms for the maximum clique problem over a large range of the commonly used DIMACS benchmark instances.

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