Adaptive, Restart, Randomized Greedy Heuristics for Maximum Clique

  • Authors:

  • Arun Jagota;Laura A. Sanchis

  • Affiliations:

  • Department of Computer Engineering, Baskin School of Engineering, University of California, Santa Cruz, CA 95064;Department of Computer Science, Colgate University, Hamilton, NY 13346

  • Venue:
  • Journal of Heuristics
  • Year:
  • 2001

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Abstract

This paper presents some adaptive restart randomized greedy heuristics for MAXIMUM CLIQUE. The algorithms are based on improvements and variations of previously-studied algorithms by the authors. Three kinds of adaptation are studied: adaptation of the initial state (AI) given to the greedy heuristic, adaptation of vertex weights (AW) on the graph, and no adaptation (NA). Two kinds of initialization of the vertex-weights are investigated: unweighted initialization (wi := 1) and degree-based initialization (wi := di where di is the degree of vertex i in the graph). Experiments are conducted on several kinds of graphs (random, structured) with six combinations: {NA, AI, and AW} × {unweighted initialization, degree-based initialization}. A seventh state of the art semi-greedy algorithm, DMclique, is evaluated as a benchmark algorithm. We concentrate on the problem of finding large cliques in large, dense graphs in a relatively short amount of time. We find that the different strategies produce different effects, and that different algorithms work best on different kinds of graphs.