Integral infeasibility and testing total dual integrality

  • Authors:

  • David L. Applegate;William Cook;S.Thomas Mccormick

  • Affiliations:

  • Department of Computer Science, Carnegie Mellon University, Pittsburgh, PA 15213, USA;Bell Communications Research, Morristown, NJ 07690, USA;Faculty of Commerce & Business Administration, University of British Columbia, Vancouver, B.C. V6T 1Y8 Canada

  • Venue:
  • Operations Research Letters
  • Year:
  • 1991

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Abstract

A number of well known results in combinatorial optimization, such as Hoffman's circulation theorem and the matching theorems of Hall and Tutte, can be interpreted as stating that either a certain linear system has a solution or there exists a simple combinatorial reason why it is infeasible. We give a characterization of total dual integrality in terms of such infeasibility results. This leads to a method for testing total dual integrality which is tractable for small linear systems. In particular, a computer implementation of the method settled a conjecture of Barahona and Mahjoub concerning feedback sets in directed graphs.