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Extension of the parallel nested dissection algorithm to path algebra problems

  • Victor Pan
  • John Reif
Session 8 Parallel Algorithms
Part of the Lecture Notes in Computer Science book series (LNCS, volume 241)

Abstract

This paper extends the author's parallel nested dissection algorithm of [PR] originally devised for solving sparse linear systems. We present a class of new applications of the nested dissection method, this time to path algebra computations, (in both cases of single source and all pair paths), where the path algebra problem is defined by a symmetric matrix A whose associated graph G with n vertices is planar. We substantially improve the known algorithms for path algebra problems of that general class: {fx470-1}

(In case of parallel algorithms we assume that G is given with its \({\text{O(}}\sqrt {\text{n}} )\)-separator family.) Further applications lead, in particular, to computing a maxflow and a mincut in an undirected planar network using O(log4n) parallel steps, n1.5/log n processors or alternatively O(log3n) steps, n2/log n processors, versus the known bounds, O(log2n) and n4, of [JV].

Keywords

Short Path Planar Graph Parallel Algorithm Short Path Problem Path Algebra 
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 1986

Authors and Affiliations

  • Victor Pan
    • 1
  • John Reif
    • 2
  1. 1.Computer Science DepartmentState University of New York at AlbanyAlbany
  2. 2.Aiken Computation Lab. Division of Applied SciencesHarvard UniversityCambridge

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