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Fast RNC and NC algorithms for finding a maximal set of paths with an application

  • Ryuhei Uehara
  • Zhi-Zhong Chen
  • Xin He
Session 6
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1090)

Abstract

We present two parallel algorithms for finding a maximal set of paths in a given undirected graph. The former runs in O(log n) expected time with O(n + m) processors on a CRCW PRAM. The latter runs in O(log2n) time with O2(n + m)/log n) processors on an EREW PRAM. The results improve on the best previous ones and can also be extended to digraphs. We then use the results to design an NC approximation algorithm for a variation of the shortest superstring problem introduced by Jiang et al. The approximation algorithm achieves a compression ratio of \(\frac{1}{{3 + \varepsilon }}\)for any ε >0.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Ryuhei Uehara
    • 1
  • Zhi-Zhong Chen
    • 2
  • Xin He
    • 3
  1. 1.Center for Inform. Sci.Tokyo Woman's Christian Univ.Tokyo
  2. 2.Dept. of Math. Sci.Tokyo Denki Univ.SaitamaJapan
  3. 3.Dept. of Comput. Sci.SUNY at BuffaloBuffaloUSA

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