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Minimum s-t cut of a planar undirected network in o(n log2(n)) time

  • John H. Reif
Session 2: F.P. Preparata, Chairman
Part of the Lecture Notes in Computer Science book series (LNCS, volume 115)

Abstract

Let N be a planar undirected network with distinguished vertices s, t, a total of n vertices, and each edge labeled with a positive real (the edge's cost) from a set L. This paper presents an algorithm for computing a minimum (cost) s-t cut of N. For general L, this algorithm runs in time O(n log2(n)) time on a (uniform cost criteria) RAM. For the case L contains only integers ≤n0(1), the algorithm runs in time O(n log(n)loglog(n)). Our algorithm also constructs a minimum s-t cut of a planar graph (i.e., for the case L= {1}) in time O(n log(n)).

The fastest previous algorithm for computing a minimum s-t cut of a planar undirected network [Gomory and Hu, 1961] and [Itai and Shiloach, 1979] has time O(n2 log(n)) and the best previous time bound for minimum s-t cut of a planar graph (Cheston, Probert, and Saxton, 1977] was O(n2).

Keywords

Planar Graph Multiple Edge Planar Network Recursive Call Dual Graph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1981

Authors and Affiliations

  • John H. Reif
    • 1
  1. 1.Aiken Computation LaboratoryHarvard UniversityCambridgeUSA

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