Issue No. 12 - December (1991 vol. 40)

ISSN: 0018-9340

pp: 1413-1418

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/12.106226

ABSTRACT

<p>A Boltzmann machine architecture to solve the problems of maximum independent set, set partitioning, clique, minimum vertex cover, minimum set cover, and maximum set packing is described. The authors evaluate the maximum and the average error of the method where the error is defined as the ratio of the cardinality of the obtained solution for an instance with respect to the optimal one. The results are compared with those obtained from the implementation of the heuristic described by D.S. Johnson (1974). The model treats the general case of all these problems that is the case when costs are associated with the data (vertices or subsets). The unweighted case becomes a particular case in this approach. It is shown that the model finds optimal solutions for a large percentage of the treated instances and provides a good performance ratio for the rest.</p>

INDEX TERMS

approximation; NP-complete problems; Boltzmann machine method; covering; packing problems; maximum independent set; set partitioning; clique; minimum vertex cover; minimum set cover; optimal solutions; combinatorial mathematics; computational complexity; heuristic programming; neural nets; parallel architectures.

CITATION

V. Zissimopoulos, V.T. Paschos, F. Pekergin, "On the Approximation of NP-Complete Problems by Using the Boltzmann Machine Method: The Cases of Some Covering and Packing Problems",

*IEEE Transactions on Computers*, vol. 40, no. , pp. 1413-1418, December 1991, doi:10.1109/12.106226