Flow network reduction for unique topological ordering

  • Authors:
  • H. Koh

  • Affiliations:
  • Department of Computer Science, Lamar University, Beaumont, Texas

  • Venue:
  • CSC '89 Proceedings of the 17th conference on ACM Annual Computer Science Conference
  • Year:
  • 1989

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Abstract

This paper describes a more restrictive definition of cutsets as they are found useful in solving certain problems and presents a reduction method to reduce a flow network (an acyclic weighted digraph) with multiple topological orderings of vertices so that (1) the resulting reduced network has only one topological ordering and (2) the original network and the reduced network have the same maximal cutset. The motivation for such a reduction method is that if a network has only one topological ordering then the maximal cutset can be found in a linear time (linear in terms of the number of arcs).