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Online and Offline Distance Constrained Labeling of Disk Graphs

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Algorithms — ESA 2001 (ESA 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2161))

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Abstract

A disk graph is the intersection graph of a set of disks in the plane. We consider the problem of assigning labels to vertices of a disk graph satisfying a sequence of distance constrains. Our objective is to minimize the distance between the smallest and the largest labels. We propose an on-line labeling algorithm on disk graphs, if the maximum and minimum diameters are bounded. We give the upper and lower bounds on its competitive ratio, and show that the algorithm is asymptotically optimal. In more detail we explore the case of distance constraints (2,1), and present two off-line approximation algorithms. The last one we call robust, i.e. it does not require the disks representation and either outputs a feasible labeling, or answers the input is not a unit disk graph.

Partially supported by EU ARACNE project HPRN-CT-1999-00112, by GACR 201/99/0242 and by the Ministry of Education of the Czech Republic as project LN00A056.

Partially supported by the DFG-Graduiertenkolleg “Effiziente Algorithmen und Mehrskalenmethoden”.

The work of this author was done while he was a visiting postdoc at DIMATIA-ITI partially supported by GAČR 201/99/0242 and by the Ministry of Education of the Czech Republic as project LN00A056. Also supported by Netherlands Organization for Scientific Research (NWO grant 047.008.006.)

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Author information

Authors and Affiliations

  1. CAU, Institute of Computer Science and Applied Mathematics, Olshausenstr. 40, 24098, Kiel, Germany

    Jiří Fiala & Aleksei V. Fishkin

  2. Faculty of Mathematics and Physics, Institute for Theoretical Computer Science (ITI), Charles University, Malostranské nám. 2/25, 118 00, Prague, Czech Republic

    Jiří Fiala

  3. Faculty of Mathematics and Mechanics, St. Petersburg State University, Bibliotechnaya sq. 2, St. Petersburg, 198904, Russia

    Fedor V. Fomin

Authors
  1. Jiří Fiala
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  2. Aleksei V. Fishkin
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  3. Fedor V. Fomin
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Editor information

Editors and Affiliations

  1. Department of Mathematics and Computer Science and Heinz Nixdorf Institute, Paderborn University, 33095, Paderborn, Germany

    Friedhelm Meyer auf der Heide

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© 2001 Springer-Verlag Berlin Heidelberg

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Fiala, J., Fishkin, A.V., Fomin, F.V. (2001). Online and Offline Distance Constrained Labeling of Disk Graphs. In: auf der Heide, F.M. (eds) Algorithms — ESA 2001. ESA 2001. Lecture Notes in Computer Science, vol 2161. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44676-1_39

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  • DOI: https://doi.org/10.1007/3-540-44676-1_39

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42493-2

  • Online ISBN: 978-3-540-44676-7

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