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A new simple parallel tree contraction scheme and its application on distance-hereditary graphs

  • Sun-Yuan Hsieh
  • Chin-Wen Hoe
  • Tsan-Sheng Hsu
  • Ming-Tat Ko
  • Gen-Huey Chen
Regular Talks
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1457)

Abstract

We present a new parallel tree contraction scheme which takes O(log n) contraction phases to reduce a tree to its root, and implement this scheme in O(log n log log n) time using O(n/ log log n) processors on an arbitrary CROW PRAM. We then show a data structure to represent a connected distance-hereditary graph G in the form of a rooted tree. Applying our tree contraction scheme on the above data structure together with graph theoretical properties, we solve the problems of finding a minimum connected γ-dominating set and finding a minimum γ-dominating clique on G in O(log n log log n) time using O((n + m) /log log n) processors on an arbitrary CROW PRAM, where n and m are the number of vertices and edges in G, respectively.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Sun-Yuan Hsieh
    • 1
  • Chin-Wen Hoe
    • 2
  • Tsan-Sheng Hsu
    • 3
  • Ming-Tat Ko
    • 3
  • Gen-Huey Chen
    • 1
  1. 1.Department of Computer Science and Information EngineeringNational Taiwan UniversityTaipeiTaiwan, ROC
  2. 2.Department of Computer Science and Information EngineeringNational Central UniversityChung-LiTaiwan, ROC
  3. 3.Institute of Information ScienceAcademia SinicaTaipeiTaiwan, ROC

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