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Solving cheap graph problems on Meshes

  • Jop F. Sibeyn
  • Michael Kaufmann
Contributed Papers Distributed Computation
  • 918 Downloads
Part of the Lecture Notes in Computer Science book series (LNCS, volume 969)

Abstract

Efficient mesh algorithms exist for ‘expensive’ graph problems like transitive closure and computing all shortest paths, taking O(n) time on an n×n mesh for a graph with n vertices. This is work-optimal. On the other hand, there are so far no efficient algorithms for ‘cheap’ graph problems like finding the connected components, constructing a minimum spanning tree, or finding a path between a pair of vertices. These problems are cheap in the sense that sequentially they can be solved in time (almost) linear in n and m, where m is the number of edges.

In this paper we show that the mentioned cheap problems can be solved on an √N×√N mesh in O((n·m/N)1/2+ log n· (√N+m/N)) time. We derive a lower bound of Ω((n·m/N)1/2+√N+m/N). Hence, the algorithms have optimal time order for most n,m and N. The algorithms are work-optimal to within a factor log n for N≤m/n.

Keywords

Span Tree Minimum Span Tree List Ranking Sparse Graph Graph Problem 
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 1995

Authors and Affiliations

  • Jop F. Sibeyn
    • 1
  • Michael Kaufmann
    • 2
  1. 1.Max-Planck-Institut für Informatik, Im StadtwaldSaarbrückenGermany
  2. 2.Fakultät InformatikUniversität TübingenTübingenGermany

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