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Range Searching in Categorical Data: Colored Range Searching on Grid

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Algorithms — ESA 2002 (ESA 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2461))

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Abstract

Range searching, a fundamental problem in numerous applications areas, has been widely studied in computational geometry and spatial databases. Given a set of geometric objects, a typical range query asks for reporting all the objects that intersect a query object. However in many applications, including databases and network routing, input objects are partitioned into categories and a query asks for reporting the set of categories of objects that intersect a query object. Moreover in many such applications, objects lie on a grid. We abstract the category of an object by associating a color with each object. In this paper, we present efficient data structures for solving the colored range-searching and colored point-enclosure problem on U x U grid. Our data structures use near- linear space and answer a query in O(log log U +k) time, where k is the output size. As far as we know, this is the first result on colored range-searching for objects lying on a grid.

Research by the first two authors is supported by NSF under grants CCR-00-86013 EIA-98-70724, EIA-01-31905, and CCR-97-32787, and by a grant from the U.S.- Israel Binational Science Foundation. Part of this work was done when the second author was visiting the third author at DIMACS.

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Author information

Authors and Affiliations

  1. Department of Computer Science, Duke University, 27708, Durham, NC

    Pankaj K. Agarwal & Sathish Govindarajan

  2. Shannon Laboratory, AT&T Labs, 180 Park Ave., 07932, Florham Park, NJ

    S. Muthukrishnan

Authors
  1. Pankaj K. Agarwal
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  2. Sathish Govindarajan
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  3. S. Muthukrishnan
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Editor information

Editors and Affiliations

  1. Fakultät II: Mathematik und Naturwissenschaften, Technische Universität Berlin, Strasse des 17. Juni 136, 10623, Berlin, Germany

    Rolf Möhring

  2. Department of Mathematics and Computer Science, University of Leicester, University Road, LE1 7RH, Leicester, UK

    Rajeev Raman

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© 2002 Springer-Verlag Berlin Heidelberg

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Agarwal, P.K., Govindarajan, S., Muthukrishnan, S. (2002). Range Searching in Categorical Data: Colored Range Searching on Grid. In: Möhring, R., Raman, R. (eds) Algorithms — ESA 2002. ESA 2002. Lecture Notes in Computer Science, vol 2461. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45749-6_6

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  • DOI: https://doi.org/10.1007/3-540-45749-6_6

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-44180-9

  • Online ISBN: 978-3-540-45749-7

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