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Dynamic Connectivity for Axis-Parallel Rectangles

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Algorithms – ESA 2006 (ESA 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4168))

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Abstract

In this paper we give a fully dynamic data structure to maintain the connectivity of the intersection graph of n axis-parallel rectangles. The amortized update time (insertion and deletion of rectangles) is O(n 10/11polylog n) and the query time (deciding whether two given rectangles are connected) is O(1). It slightly improves the update time (O(n 0.94)) of the previous method while drastically reducing the query time (near O(n 1/3)). Our method does not use fast matrix multiplication results and supports a wider range of queries.

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Author information

Authors and Affiliations

  1. School of Computer Science, University of Waterloo, Waterloo, Ontario, N2L 3G1, Canada

    Peyman Afshani & Timothy M. Chan

Authors
  1. Peyman Afshani
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  2. Timothy M. Chan
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Editors and Affiliations

  1. Microsoft Research, One Microsoft Way, Redmond, WA 98052, USA and School of Computer Science, Tel-Aviv University, 69978, Tel-Aviv, Israel

    Yossi Azar

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

    Thomas Erlebach

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© 2006 Springer-Verlag Berlin Heidelberg

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Afshani, P., Chan, T.M. (2006). Dynamic Connectivity for Axis-Parallel Rectangles. In: Azar, Y., Erlebach, T. (eds) Algorithms – ESA 2006. ESA 2006. Lecture Notes in Computer Science, vol 4168. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11841036_5

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  • DOI: https://doi.org/10.1007/11841036_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-38875-3

  • Online ISBN: 978-3-540-38876-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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