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V. Zissimopoulos, V.T. Paschos, F. Pekergin, "On the Approximation of NPComplete Problems by Using the Boltzmann Machine Method: The Cases of Some Covering and Packing Problems," IEEE Transactions on Computers, vol. 40, no. 12, pp. 14131418, December, 1991.  
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@article{ 10.1109/12.106226, author = {V. Zissimopoulos and V.T. Paschos and F. Pekergin}, title = {On the Approximation of NPComplete Problems by Using the Boltzmann Machine Method: The Cases of Some Covering and Packing Problems}, journal ={IEEE Transactions on Computers}, volume = {40}, number = {12}, issn = {00189340}, year = {1991}, pages = {14131418}, doi = {http://doi.ieeecomputersociety.org/10.1109/12.106226}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
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TY  JOUR JO  IEEE Transactions on Computers TI  On the Approximation of NPComplete Problems by Using the Boltzmann Machine Method: The Cases of Some Covering and Packing Problems IS  12 SN  00189340 SP1413 EP1418 EPD  14131418 A1  V. Zissimopoulos, A1  V.T. Paschos, A1  F. Pekergin, PY  1991 KW  approximation; NPcomplete 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. VL  40 JA  IEEE Transactions on Computers ER   
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.
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