Mathematical Programming

, Volume 33, Issue 1, pp 28–42

On the acyclic subgraph polytope

  • Martin Grötschel
  • Michael Jünger
  • Gerhard Reinelt
Article

DOI: 10.1007/BF01582009

Cite this article as:
Grötschel, M., Jünger, M. & Reinelt, G. Mathematical Programming (1985) 33: 28. doi:10.1007/BF01582009

Abstract

The acyclic subgraph problem can be formulated as follows. Given a digraph with arc weights, find a set of arcs containing no directed cycle and having maximum total weight. We investigate this problem from a polyhedral point of view and determine several classes of facets for the associated acyclic subgraph polytope. We also show that the separation problem for the facet defining dicycle inequalities can be solved in polynomial time. This implies that the acyclic subgraph problem can be solved in polynomial time for weakly acyclic digraphs. This generalizes a result of Lucchesi for planar digraphs.

Key words

Acyclic Subgraph ProblemFeedback Arc Set ProblemFacets of PolyhedraPolynomial Time AlgorithmsWeakly Acyclic Digraphs

Copyright information

© The Mathematical Programming Society, Inc. 1985

Authors and Affiliations

  • Martin Grötschel
    • 1
  • Michael Jünger
    • 1
  • Gerhard Reinelt
    • 1
  1. 1.Institut für MathematikUniversität AugsburgAugsburgFR Germany