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f-Sensitivity Distance Oracles and Routing Schemes

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Algorithms – ESA 2010 (ESA 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6346))

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Abstract

An f-sensitivity distance oracle for a weighted undirected graph G(V,E) is a data structure capable of answering restricted distance queries between vertex pairs, i.e., calculating distances on a subgraph avoiding some forbidden edges. This paper presents an efficiently constructible f-sensitivity distance oracle that given a triplet (s,t,F), where s and t are vertices and F is a set of forbidden edges such that |F| ≤ f, returns an estimate of the distance between s and t in G(V,E ∖ F). For an integer parameter k ≥ 1, the size of the data structure is O(fkn 1 + 1/klog(nW)), where W is the heaviest edge in G, the stretch (approximation ratio) of the returned distance is (8k − 2)(f + 1), and the query time is O(|F|·log2 n·loglogn·loglogd), where d is the distance between s and t in G(V,E ∖ F).

The paper also considers f-sensitive compact routing schemes, namely, routing schemes that avoid a given set of forbidden (or failed) edges. It presents a scheme capable of withstanding up to two edge failures. Given a message M destined to t at a source vertex s, in the presence of a forbidden edge set F of size |F| ≤ 2 (unknown to s), our scheme routes M from s to t in a distributed manner, over a path of length at most O(k) times the length of the optimal path (avoiding F). The total amount of information stored in vertices of G is O(k n 1 + 1/klog(nW)logn).

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Author information

Authors and Affiliations

  1. Department of Computer Science, The Weizmann Institute, Rehovot, Israel

    Shiri Chechik & David Peleg

  2. Computer Science Division, Open University of Israel, Raanana, Israel

    Michael Langberg

  3. Department of Computer Science, Bar-Ilan University, Ramat-Gan, Israel

    Liam Roditty

Authors
  1. Shiri Chechik
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  2. Michael Langberg
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  3. David Peleg
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  4. Liam Roditty
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Editor information

Editors and Affiliations

  1. Department of Mathematics and Computing Science, TU Eindhoven, Eindhoven, The Netherlands

    Mark de Berg

  2. Institute for Computer Science, J.W. Goethe University, 60325, Frankfurt/Main, Germany

    Ulrich Meyer

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Chechik, S., Langberg, M., Peleg, D., Roditty, L. (2010). f-Sensitivity Distance Oracles and Routing Schemes. In: de Berg, M., Meyer, U. (eds) Algorithms – ESA 2010. ESA 2010. Lecture Notes in Computer Science, vol 6346. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15775-2_8

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  • DOI: https://doi.org/10.1007/978-3-642-15775-2_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-15774-5

  • Online ISBN: 978-3-642-15775-2

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