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Communication-efficient parallel multiway and approximate minimum cut computation

  • Friedhelm Meyer auf der Heide
  • Gabriel Terán Martinez
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1380)

Abstract

We examine different variants of minimum cut problems on undirected weighted graphs on the p-processor bulk synchronous parallel (BSP) model of Valiant. This model and the corresponding cost measure guide algorithm designers to develop work efficient algorithms that need only very little communication. Karger and Stein have presented a recursive contraction algorithm to solve minimum cut problems. They suggest a PRAM implementation of their algorithm working in polynomial polylogarithmic time, but being not work-optimal. Typically the problem size n is much larger than the number of processors p on real-world parallel computers (pn). For this setting we present improved BSP implementations of the algorithm of Karger and Stein. For the case of multiway cut and approximate minimum cut we obtain optimal, communication efficient results. A nice effect, beside the optimality, is that communication is efficient for a large spectrum of BSP-parameters. In the case of the minimal cut problem our results are close to optimal.

Keywords

Computation Tree Bulk Synchronous Parallel Undirected Weighted Graph Communication Volume Parallel Random Access Machine 
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 1998

Authors and Affiliations

  • Friedhelm Meyer auf der Heide
    • 1
  • Gabriel Terán Martinez
    • 1
  1. 1.Heinz Nixdorf Institute and Department of Computer ScienceUniversity of PaderbornPaderbornGermany

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