Document Type
Article
Publication Date
7-13-1998
Abstract
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 NP complete, 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.
Recommended Citation
Rader, David J. and Hammer, Peter L., "Maximally Disjoint Solutions of the Set Covering Problem" (1998). Mathematical Sciences Technical Reports (MSTR). 110.
https://scholar.rose-hulman.edu/math_mstr/110
Included in
Applied Mathematics Commons, Discrete Mathematics and Combinatorics Commons, Operations Research, Systems Engineering and Industrial Engineering Commons, Theory and Algorithms Commons
Comments
MSTR 98-03