, Volume 7, Issue 2, pp 131144
First online:
Maximally Disjoint Solutions of the Set Covering Problem
 Peter L. HammerAffiliated withRUTCOR, Rutgers University
 , David J. RaderJr.Affiliated withDepartment of Mathematics, RoseHulman Institute of Technology
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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.
 Title
 Maximally Disjoint Solutions of the Set Covering Problem
 Journal

Journal of Heuristics
Volume 7, Issue 2 , pp 131144
 Cover Date
 200103
 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