Weighted and Unweighted Maximum Clique Algorithms with Upper Bounds from Fractional Coloring
CARNEGIE-MELLON UNIV PITTSBURGH PA MANAGEMENT SCIENCES RESEARCH GROUP
Pagination or Media Count:
The linear programming relaxation of the minimum vertex coloring problem, called the fractional coloring problem, is NP-hard. We describe efficient approximation procedures for both the weighted and unweighted versions of the problem. These fractional coloring procedures are then used for generating upper bounds for the weighted or unweighted maximum clique problem in the framework of a branch and bound procedure. Extensive computational testing shows that replacing the standard upper bounding procedures based on various integer coloring heuristics with the somewhat more expensive fractional coloring procedure results in improvements of the bound by up to one fourth in the unweighted and up to one fifth in the weighted case, accompanied by a decrease in the size of the search tree by a factor of almost two.
- Operations Research
- Computer Programming and Software