On the Set Covering Problem. II. An Algorithm.
Abstract
In an earlier paper the authors proved that any feasible integer solution to the linear program associated with the equality-constrained set covering problem can be obtained from any other feasible integer solution by a sequence of less than m pivots (where m is the number of equations), such that each solution generated in the sequence is integer. However, degeneracy makes it difficult to find a sequence of pivots leading to an integer optimum. In the paper the authors give a constructive characterization of adjacency relations between integer vertices of the feasible set, which enables them to generate edges (all, if necessary) connecting a given integer vertex to adjacent integer vertices. This helps overcome the difficulties caused by degeneracy and leads to a class of algorithms of which two are discussed. (Author Modified Abstract)
Document Details
- Document Type
- Technical Report
- Publication Date
- Nov 01, 1972
- Accession Number
- AD0757428
Entities
People
- Egon Balas
- Manfred Padberg
Organizations
- Carnegie Mellon University