Algorithmica

, Volume 29, Issue 4, pp 610–637

Reactive Local Search for the Maximum Clique Problem1

  • R. Battiti
  • M. Protasi
Article

Abstract.

A new Reactive Local Search (\RLS ) algorithm is proposed for the solution of the Maximum-Clique problem. \RLS is based on local search complemented by a feedback (history-sensitive) scheme to determine the amount of diversification. The reaction acts on the single parameter that decides the temporary prohibition of selected moves in the neighborhood, in a manner inspired by Tabu Search. The performance obtained in computational tests appears to be significantly better with respect to all algorithms tested at the the second DIMACS implementation challenge. The worst-case complexity per iteration of the algorithm is O(max {n,m}) where n and m are the number of nodes and edges of the graph. In practice, when a vertex is moved, the number of operations tends to be proportional to its number of missing edges and therefore the iterations are particularly fast in dense graphs.

Key words. Maximum-clique problem, Heuristic algorithms, Tabu search, Reactive search. 

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Copyright information

© Springer-Verlag 2001

Authors and Affiliations

  • R. Battiti
    • 1
  • M. Protasi
    • 2
  1. 1.Dipartimento di Matematica, Universitá of Trento, Via Sommarive 14, 38050 Povo (Trento), Italy. battiti@ science.unitn.it.IT
  2. 2.Dipartimento di Matematica, Universitá di Roma ``Tor Vergata'', Roma, Italy. Marco died on February 1, 1998.IT

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