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A Quasi-Polynomial Time Partition Oracle for Graphs with an Excluded Minor

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Automata, Languages, and Programming (ICALP 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7965))

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Abstract

Motivated by the problem of testing planarity and related properties, we study the problem of designing efficient partition oracles. A partition oracle is a procedure that, given access to the incidence lists representation of a bounded-degree graph G = (V,E) and a parameter ε, when queried on a vertex v ∈ V, returns the part (subset of vertices) which v belongs to in a partition of all graph vertices. The partition should be such that all parts are small, each part is connected, and if the graph has certain properties, the total number of edges between parts is at most ε|V|. In this work we give a partition oracle for graphs with excluded minors whose query complexity is quasi-polynomial in 1/ε, thus improving on the result of Hassidim et al. (Proceedings of FOCS 2009) who gave a partition oracle with query complexity exponential in 1/ε. This improvement implies corresponding improvements in the complexity of testing planarity and other properties that are characterized by excluded minors as well as sublinear-time approximation algorithms that work under the promise that the graph has an excluded minor.

A full version of this paper appears in [14].

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Author information

Authors and Affiliations

  1. School of Computer Science, Tel Aviv University, Tel Aviv, 69978, Israel

    Reut Levi

  2. School of Electrical Engineering, Tel Aviv University, Tel Aviv, 69978, Israel

    Dana Ron

Authors
  1. Reut Levi
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  2. Dana Ron
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Editor information

Editors and Affiliations

  1. Department of Informatics, University of Bergen, Postboks 7803, 5020, Bergen, Norway

    Fedor V. Fomin

  2. Faculty of Computing, University of Latvia, Raina bulv. 19, 1586, Riga, Latvia

    Rūsiņš Freivalds

  3. Department of Computer Science, University of Oxford, Wolfson Building, Parks Road, OX1 3QD, Oxford, UK

    Marta Kwiatkowska

  4. Faculty of Mathematics and Computer Science, Weizmann Institute of Science, POB 26, 76100, Rehovot, Israel

    David Peleg

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Levi, R., Ron, D. (2013). A Quasi-Polynomial Time Partition Oracle for Graphs with an Excluded Minor. In: Fomin, F.V., Freivalds, R., Kwiatkowska, M., Peleg, D. (eds) Automata, Languages, and Programming. ICALP 2013. Lecture Notes in Computer Science, vol 7965. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39206-1_60

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  • DOI: https://doi.org/10.1007/978-3-642-39206-1_60

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-39205-4

  • Online ISBN: 978-3-642-39206-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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