Maximally Disjoint Solutions of the Set Covering Problem
 Peter L. Hammer,
 David J. Rader Jr.
 … show all 2 hide
Rent the article at a discount
Rent now* Final gross prices may vary according to local VAT.
Get AccessAbstract
This paper is concerned with finding two solutions of a set covering problem that have a minimum number of variables in common. We show that this problem is NPcomplete, even in the case where we are only interested in completely disjoint solutions. We describe three heuristic methods based on the standard greedy algorithm for set covering problems. Two of these algorithms find the solutions sequentially, while the third finds them simultaneously. A local search method for reducing the overlap of the two given solutions is then described. This method involves the solution of a reduced set covering problem. Finally, extensive computational tests are given demonstrating the nature of these algorithms. These tests are carried out both on randomly generated problems and on problems found in the literature.
 Balas, E., Ho, A. (1980) Set Covering Algorithms Using Cutting Planes, Heuristics, and Subgradient Optimization: A Computational Study. Math. Programming Study 12: pp. 3760
 Bard, J.F., Feo, T.A. (1987) Minimizing the Acquisition Cost of Flexible Manufacturing Equipment. Technical Report. Operations Research Group, Department of Mechanical Engineering, The University of Texas at Austin, Austin, TXpp. 78712
 Bard, J.F., Feo, T.A. (1989) Operations Sequencing in Discrete Parts Manufacturing. Management Science 35: pp. 249255
 Beasley, J.E. (1987) An Algorithm for Set Covering Problem. European Journal of Operational Research 31: pp. 8593
 Beasley, J.E. (1990) ORLibrary: Distributing Test Problems By Electronic Mail. J. Oper. Res. Soc. 41: pp. 10691072
 Beasley, J.E., Chu, P.C. (1996) A Genetic Algorithm for the Set Covering Problem. European Journal of Operational Research 94: pp. 392404
 Brass, P., Harborth, H., Nienborg, H. (1995) On the Maximum Number of Edges in a C4free Subgraph.. J. Graph Theory 19: pp. 1723
 Chvàtal, V. (1979) A Greedy Heuristic for the Set Covering Problem. Mathematics of Operations Research 4: pp. 233235
 Erdös, P. (1990) On Some of My Favorite Problems in Graph Theory and Block Designs. Le Matematische 45: pp. 6174
 Feo, T.A., Bard, J.F. (1987) A Network Approach to Flight Scheduling and Maintenance Base Planning. Technical Report. Operations Research Group, Department of Mechanical Engineering, The University of Texas at Austin, Austin, TXpp. 78712
 Feo, T.A., Resende, M.G.C. (1989) A Probabilistic Heuristic for a Computationally Difficult Set Covering Problem. Operations Research Letters 8: pp. 6771
 Feo, T.A., Resende, M.G.C. (1995) Greedy Randomized Adaptive Search Procedures. Journal of Global Optimization 6: pp. 109133
 Garey, M.R., Johnson, D.S. (1979) Computers and Intractability: A Guide to the Theory of NPCompleteness. W.H. Freeman and Company, New York
 Goldberg, M.K., Russell, H.C. (1995) Toward Computing m (4). Ars Combinatoria 3: pp. 139148
 Grossman, T., Wool, A. (1997) Computational Experience with Approximation Algorithms for the Set Covering Problem. European Journal of Operational Research 101: pp. 8192
 Harborth, H., Nienborg, H. (1994) Maximum Number of Edges in a Sixcube Without Fourcycles. Bull. Inst. Combin. 12: pp. 5560
 Title
 Maximally Disjoint Solutions of the Set Covering Problem
 Journal

Journal of Heuristics
Volume 7, Issue 2 , pp 131144
 Cover Date
 20010301
 DOI
 10.1023/A:1009687403254
 Print ISSN
 13811231
 Online ISSN
 15729397
 Publisher
 Kluwer Academic Publishers
 Additional Links
 Topics
 Keywords

 set covering
 disjoint solutions
 GRASP algorithm
 Industry Sectors
 Authors

 Peter L. Hammer ^{(1)}
 David J. Rader Jr. ^{(2)}
 Author Affiliations

 1. RUTCOR, Rutgers University, 640 Bartholomew Rd., Piscataway, NJ, 08854, USA
 2. Department of Mathematics, RoseHulman Institute of Technology, Terre Haute, In, 47803, USA