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The Multi-radius Cover Problem

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Algorithms and Data Structures (WADS 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3608))

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Abstract

Let G = (V,E) be a graph with a non-negative edge length l u,v for every (u,v) ∈ E. The vertices of G represent locations at which transmission stations are positioned, and each edge of G represents a continuum of demand points to which we should transmit. A station located at v is associated with a set R v of allowed transmission radii, where the cost of transmitting to radius r ∈ R v is given by c v (r). The multi-radius cover problem asks to determine for each station a transmission radius, such that for each edge (u,v) ∈ E the sum of the radii in u and v is at least l u,v , and such that the total cost is minimized.

In this paper we present LP-rounding and primal-dual approximation algorithms for discrete and continuous variants of multi-radius cover. Our algorithms cope with the special structure of the problems we consider by utilizing greedy rounding techniques and a novel method for constructing primal and dual solutions.

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Authors and Affiliations

  1. School of Mathematical Sciences, Tel-Aviv University, Tel-Aviv, 69978, Israel

    Refael Hassin & Danny Segev

Authors
  1. Refael Hassin
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  2. Danny Segev
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Editors and Affiliations

  1. Carleton University, Ottawa, Canada

    Frank Dehne

  2. Cheriton School of Computer Science, University of Waterloo, N2L 3G1, Waterloo, Ont., Canada

    Alejandro López-Ortiz

  3. School of Computer Science, Carleton University, 1125 Colonel By Drive, K1S 5B6, Ottawa, Canada

    Jörg-Rüdiger Sack

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© 2005 Springer-Verlag Berlin Heidelberg

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Hassin, R., Segev, D. (2005). The Multi-radius Cover Problem. In: Dehne, F., López-Ortiz, A., Sack, JR. (eds) Algorithms and Data Structures. WADS 2005. Lecture Notes in Computer Science, vol 3608. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11534273_4

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  • DOI: https://doi.org/10.1007/11534273_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-28101-6

  • Online ISBN: 978-3-540-31711-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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