A quadratic 0-1 optimization algorithm for the maximum clique and stable set problems
It is well known that several combinatorial optimization problems can be readily and nicely modeled as appropriately defined quadratic 0-1 functions to be optimized. In this paper we present an algorithm for minimizing general quadratic 0-1 functions and, indirectly, any problem (such as the maximum stable set and the maximum clique problems) which is reducible to this model. The algorithm we present uses a bounding procedure based on two simple quadratic 0-1 identities. When interpreted in the context of the maximum stable set and clique problems, this procedure can be viewed as computing packings of edges, odd cycles and odd homeomorphs of K{sub 4}. In this paper we also report on the computational experiments carried out on 44 DIMACS clique benchmark instances and 15 randomly generated clique instances with 90% density and up to 200 nodes. Ours is a general-purpose algorithm that has proved to be effective in solving the maximum stable set and clique problems via quadratic 0-1 optimization.
- OSTI ID:
- 35856
- Report Number(s):
- CONF-9408161--
- Country of Publication:
- United States
- Language:
- English
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