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Characterization of Efficiently Parallel Solvable Problems on a Class of Decomposable Graphs

  • Sun-Yuan Hsieh
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3036)

Abstract

In this paper, we sketch characteristics of those problems which can be systematically solved on decomposable graphs. Trees, series-parallel graphs, outerplanar graphs, and bandwidth-k graphs all belong to decomposable graphs. Let T d (|V|,|E|) and P d (|V|,|E|) denote the time complexity and processor complexity required to construct a parse tree representation T G for a decomposable G=(V,E) on a PRAM model M d . We define a general problem-solving paradigm to solve a wide class of subgraph optimization problems on decomposable graphs in O(T d (|V|,|E|)+log |V(T G )|) time using O(P d (|V|,|E|)+|V(T G )|/log |V(T G )|) processors on M d . By using our paradigm, we show the following parallel complexities: (a) The maximum independent set problem on trees can be solved in O(log |V|) time using O(|V|/log |V|) processors on an EREW PRAM. (b) The maximum matching problem on series-parallel graphs can be solved in O(log |E|) time using O(|E|/log |E|) processors on an EREW PRAM. (c) The efficient domination problem on series-parallel graphs can be solved in O(log |E|) time using O(|E|/log |E|) processors on an EREW PRAM.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Sun-Yuan Hsieh
    • 1
  1. 1.Department of Computer Science and Information EngineeringNational Cheng Kung UniversityTainanTaiwan

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