Batched point location in sinr diagrams via algebraic tools

Boris Aronov, Matthew J. Katz

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Abstract

    The SINR model for the quality of wireless connections has been the subject of extensive recent study. It attempts to predict whether a particular transmitter is heard at a specific location, in a setting consisting of n simultaneous transmitters and background noise. The SINR model gives rise to a natural geometric object, the SINR diagram, which partitions the space into n regions where each of the transmitters can be heard and the remaining space where no transmitter can be heard. Efficient point location in the SINR diagram, i. e., being able to build a data structure that facilitates determining, for a query point, whether any transmitter is heard there, and if so, which one, has been recently investigated in several papers. These planar data structures are constructed in time at least quadratic in n and support logarithmic-time approximate queries. Moreover, the performance of some of the proposed structures depends strongly not only on the number n of transmitters and on the approximation parameter ε, but also on some geometric parameters that cannot be bounded a priori as a function of n or ε. In this paper, we address the question of batched point location queries, i. e., answering many queries simultaneously. Specifically, in one dimension, we can answer n queries exactly in amortized polylogarithmic time per query, while in the plane we can do it approximately. All these results can handle arbitrary power assignments to the transmitters. Moreover, the amortized query time in these results depends only on n and ε. Finally, these results demonstrate the (so far underutilized) power of combining algebraic tools with those of computational geometry and other fields.

    Original languageEnglish (US)
    Title of host publicationAutomata, Languages, and Programming - 42nd International Colloquium, ICALP 2015, Proceedings
    EditorsMagnus M. Halldorsson, Naoki Kobayashi, Bettina Speckmann, Kazuo Iwama
    PublisherSpringer Verlag
    Pages65-77
    Number of pages13
    ISBN (Print)9783662476710
    DOIs
    StatePublished - Jan 1 2015
    Event42nd International Colloquium on Automata, Languages and Programming, ICALP 2015 - Kyoto, Japan
    Duration: Jul 6 2015Jul 10 2015

    Publication series

    NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
    Volume9134
    ISSN (Print)0302-9743
    ISSN (Electronic)1611-3349

    Other

    Other42nd International Colloquium on Automata, Languages and Programming, ICALP 2015
    CountryJapan
    CityKyoto
    Period7/6/157/10/15

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    ASJC Scopus subject areas

    • Theoretical Computer Science
    • Computer Science(all)

    Cite this

    Aronov, B., & Katz, M. J. (2015). Batched point location in sinr diagrams via algebraic tools. In M. M. Halldorsson, N. Kobayashi, B. Speckmann, & K. Iwama (Eds.), Automata, Languages, and Programming - 42nd International Colloquium, ICALP 2015, Proceedings (pp. 65-77). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9134). Springer Verlag. https://doi.org/10.1007/978-3-662-47672-7_6