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Labeling Schemes with Queries

  • Conference paper
Structural Information and Communication Complexity (SIROCCO 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4474))

Abstract

Recently, quite a few papers studied methods for representing network properties by assigning informative labels to the vertices of a network. Consulting the labels given to any two vertices u and v for some function f (e.g. “distance(u,v)”) one can compute the function (e.g. the graph distance between u and v). Some very involved lower bounds for the sizes of the labels were proven.

In this paper, we demonstrate that such lower bounds are very sensitive to the number of vertices consulted. That is, we show several almost trivial constructions of such labeling schemes that beat the lower bounds by large margins. The catch is that one needs to consult the labels of three vertices instead of two. We term our generalized model labeling schemes with queries.

Additional contributions are several extensions. In particular, we show that it is easy to extend our schemes for tree to work also in the dynamic scenario. We also demonstrate that the study of the queries model can help in designing a scheme for the traditional model too. Finally, we demonstrate extensions to the non-distributed environment. In particular, we show that one can preprocess a general weighted graph using almost linear space so that flow queries can be answered in almost constant time.

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Authors and Affiliations

  1. Information Systems Group, Faculty of IE&M, The Technion, Haifa, 32000, Israel

    Amos Korman & Shay Kutten

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  1. Amos Korman
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  2. Shay Kutten
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Giuseppe Prencipe Shmuel Zaks

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Korman, A., Kutten, S. (2007). Labeling Schemes with Queries. In: Prencipe, G., Zaks, S. (eds) Structural Information and Communication Complexity. SIROCCO 2007. Lecture Notes in Computer Science, vol 4474. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72951-8_10

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  • DOI: https://doi.org/10.1007/978-3-540-72951-8_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-72918-1

  • Online ISBN: 978-3-540-72951-8

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