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Logical Locality Entails Frugal Distributed Computation over Graphs (Extended Abstract)

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Graph-Theoretic Concepts in Computer Science (WG 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5911))

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Abstract

First-order logic is known to have limited expressive power over finite structures. It enjoys in particular the locality property, which states that first-order formulae cannot have a global view of a structure. This limitation ensures their low sequential computational complexity. We show that the locality impacts as well on their distributed computational complexity. We use first-order formulae to describe the properties of finite connected graphs, which are the topology of communication networks, on which the first-order formulae are also evaluated. We show that over bounded degree networks and planar networks, first-order properties can be frugally evaluated, that is, with only a bounded number of messages, of size logarithmic in the number of nodes, sent over each link. Moreover, we show that the result carries over for the extension of first-order logic with unary counting.

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Authors and Affiliations

  1. INRIA – LIAMA, Chinese Academy of Sciences, PO Box 2728, Beijing, 100080, PR China

    Stéphane Grumbach & Zhilin Wu

Authors
  1. Stéphane Grumbach
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  2. Zhilin Wu
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Editors and Affiliations

  1. CNRS - LIRMM, 161 rue Ada, 34392, Montpellier Cedex 5, France

    Christophe Paul

  2. LIAFA, case 7014, Université Paris Diderot, 75205, Paris Cedex 13, France

    Michel Habib

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Grumbach, S., Wu, Z. (2010). Logical Locality Entails Frugal Distributed Computation over Graphs (Extended Abstract). In: Paul, C., Habib, M. (eds) Graph-Theoretic Concepts in Computer Science. WG 2009. Lecture Notes in Computer Science, vol 5911. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11409-0_14

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  • DOI: https://doi.org/10.1007/978-3-642-11409-0_14

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-11408-3

  • Online ISBN: 978-3-642-11409-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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