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

Tags

DTIC Thesaurus Topics

  • Abstracts
  • Algorithms
  • Coverings
  • Equations
  • Evolutionary Algorithms
  • Heuristic Methods
  • Linear Programming
  • Mathematics
  • Sequences
  • Simplex Method

Fields of Study

  • Mathematics

Readers

  • Graph Algorithms and Convex Optimization.
  • Operations Research