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.
The linear programming relaxation of the minimum vertex coloring problem, called the fractional coloring problem, is NP-hard. We describe efficient approximation procedures
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.