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In this paper, we present a polynomial algorithm that finds an edge-maximal triangulated subgraph of an arbitrary graph. Then, we use this algorithm as a heuristic for the maximum (weight) clique problem. Finally, a local search routine is incorporated into our heuristic. Computational results comparing our algorithm with two existing edge-maximal triangulated subgraph algorithms in the literature show that the subgraphs found by our algorithm tend to contain more edges as well as a better clique of the original graph. Computational results comparing our heuristic with other heuristics, including an efficient randomized heuristic, also show the promise of our heuristic. 0 7994 John Wiley & Sons, Inc.

The linear programming relaxation of the minimum vertex coloring problem, called the fractional coloring problem, is NP-hard. We describe efficient approximation procedures

A new kind of warehouse layout problem, multiple-level warehouse layout problem (MLWLP), is investigated. Both horizontal and vertical travel costs need to be considered when making a layout. In the problem, unit travel costs are item-dependent and di erent items can be mixed in a cell. An IP model is proposed, which is shown to be NP-hard. An e ective assignment method is presented and genetic algorithm heuristics developed. Extensive computational experiments are conducted to verify the e ectiveness of the algorithms.

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The linear programming relaxation of the minimum vertex coloring problem, called the fractional coloring problem, is NP-hard. We describe efficient approximation procedures