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An Adaptive Spectral Heuristic for Partitioning Random Graphs

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Automata, Languages and Programming (ICALP 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4051))

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Abstract

We study random instances of a general graph partitioning problem: the vertex set of the random input graph G consists of k classes V 1,...,V k , and V i -V j -edges are present with probabilities p ij independently. The main result is that with high probability a partition S 1,...,S k of G that coincides with V 1,...,V k on a huge subgraph core(G) can be computed in polynomial time via spectral techniques. The result covers the case of sparse graphs (average degree O(1)) as well as the massive case (average degree #V(G)–O(1)). Furthermore, the spectral algorithm is adaptive in the sense that it does not require any information about the desired partition beyond the number k of classes.

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Authors and Affiliations

  1. Institut für Informatik, Humboldt-Universität zu Berlin, Unter den Linden 6, 10099, Berlin, Germany

    Amin Coja-Oghlan

Authors
  1. Amin Coja-Oghlan
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Editors and Affiliations

  1. Dipartimento di Informatica, Università Ca’ Foscari, Venice

    Michele Bugliesi

  2. Interdisciplinary Institute for BroadBand Technology (IBBT), Belgium

    Bart Preneel

  3. ECS, University of Southampton, UK

    Vladimiro Sassone

  4. FB Informatik, Univ. Dortmund, LS2, 44221, Dortmund, Germany

    Ingo Wegener

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© 2006 Springer-Verlag Berlin Heidelberg

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Coja-Oghlan, A. (2006). An Adaptive Spectral Heuristic for Partitioning Random Graphs. In: Bugliesi, M., Preneel, B., Sassone, V., Wegener, I. (eds) Automata, Languages and Programming. ICALP 2006. Lecture Notes in Computer Science, vol 4051. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11786986_60

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  • DOI: https://doi.org/10.1007/11786986_60

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-35904-3

  • Online ISBN: 978-3-540-35905-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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