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Solving cheap graph problems on Meshes

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Mathematical Foundations of Computer Science 1995 (MFCS 1995)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 969))

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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.

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Author information

Authors and Affiliations

  1. Max-Planck-Institut für Informatik, Im Stadtwald, 66123, Saarbrücken, Germany

    Jop F. Sibeyn

  2. Fakultät Informatik, Universität Tübingen, Sand 13, 72076, Tübingen, Germany

    Michael Kaufmann

Authors
  1. Jop F. Sibeyn
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  2. Michael Kaufmann
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Jiří Wiedermann Petr Hájek

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© 1995 Springer-Verlag Berlin Heidelberg

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Sibeyn, J.F., Kaufmann, M. (1995). Solving cheap graph problems on Meshes. In: Wiedermann, J., Hájek, P. (eds) Mathematical Foundations of Computer Science 1995. MFCS 1995. Lecture Notes in Computer Science, vol 969. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60246-1_147

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  • DOI: https://doi.org/10.1007/3-540-60246-1_147

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-60246-0

  • Online ISBN: 978-3-540-44768-9

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