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Approximation Algorithms for Spreading Points

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Approximation and Online Algorithms (WAOA 2004)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3351))

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Abstract

We consider the problem of placing n points, each one inside its own, prespecified disk, with the objective of maximizing the distance between the closest pair of them. The disks can overlap and have different sizes. The problem is NP-hard and does not admit a PTAS. In the L  ∞  metric, we give a 2-approximation algorithm running in \(O(n{\sqrt n}log^{2}n)\) time. In the L 2 metric, similar ideas yield a quadratic time algorithm that gives an \(\frac{8}{3}\)-approximation in general, and a ~ 2.2393-approximation when all the disks are congruent.

Extended abstract. A full version is available as [4]. This research was done as PhD student at the Institute of Information and Computing Sciences, Utrecht University, partially supported by Cornelis Lely Stichting, NWO, and DIMACS.

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References

  1. Aharoni, R., Haxell, P.: Hall’s theorem for hypergraphs. Journal of Graph Theory 35, 83–88 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  2. Arkin, E., Hassin, R.: Minimum diameter covering problems. Networks 36, 147–155 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  3. Baur, C., Fekete, S.: Approximation of geometric dispersion problems. Algorithmica, 30, 451–470 (2001); A preliminary version appeared In: Jansen, K., Rolim, J.D.P. (eds.) APPROX 1998. LNCS, vol. 1444, pp. 451–470. Springer, Heidelberg (1998)

    Google Scholar 

  4. Cabello, S.: Approximation algorithms for spreading points. Technical report UU-CS-2003-040 (2003), Available at http://www.cs.uu.nl/research/techreps/UU-CS-2003-040.html

  5. Cabello, S., van Kreveld, M.: Approximation algorithms for aligning points. Algorithmica 37, 211–232 (2003), A preliminary version appeared in SoCG 2003

    Article  MATH  MathSciNet  Google Scholar 

  6. Chandra, B., Halldórsson, M.M.: Approximation algorithms for dispersion problems. J. Algorithms 38, 438–465 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  7. Dent, B.: Cartography: Thematic Map Design, 5th edn. McGraw-Hill, New York (1999)

    Google Scholar 

  8. Di Battista, G., Eades, P., Tamassia, R., Tollis, I.G.: Graph Drawing. Prentice Hall, Upper Saddle River (1999)

    MATH  Google Scholar 

  9. Efrat, A., Itai, A., Katz, M.J.: Geometry helps in bottleneck matching and related problems. Algorithmica 31(1), 1–28 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  10. Fekete, S., Meijer, H.: Maximum dispersion and geometric maximum weight cliques. To appear in Algorithmica 38(3) (2004)

    Google Scholar 

  11. Fiala, J., Kratochvíl, J., Proskurowski, A.: Geometric systems of disjoint representatives. In: Goodrich, M.T., Kobourov, S.G. (eds.) GD 2002. LNCS, vol. 2528, pp. 110–117. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  12. Fiala, J., Kratochvíl, J., Proskurowski, A.: Systems of sets and their representatives. Technical Report 2002-573, KAM-DIMATIA (2002), Available at http://dimatia.mff.cuni.cz/

  13. Formann, M., Wagner, F.: A packing problem with applications to lettering of maps. In: Proc. 7th Annu. ACM Sympos. Comput. Geom., pp. 281–288 (1991)

    Google Scholar 

  14. Hassin, R., Rubinstein, S., Tamir, A.: Approximation algorithms for maximum dispersion. Operations Research Letters 21, 133–137 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  15. Megiddo, N.: Applying parallel computation algorithms in the design of serial algorithms. J. ACM 30(4), 852–865 (1983)

    Article  MATH  MathSciNet  Google Scholar 

  16. Mortensen, C.W.: Fully-dynamic two dimensional orthogonal range and line segment intersection reporting in logarithmic time. In: Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms. Society for Industrial and Applied Mathematics, pp. 618–627 (2003)

    Google Scholar 

  17. Simons, B.: A fast algorithm for single processor scheduling. In: Proc. 19th Annu. IEEE Sympos. Found. Comput. Sci., pp. 246–252 (1978)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics, Institute for Mathematics, Physics and Mechanics, Ljubljana, Slovenia

    Sergio Cabello

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  1. Sergio Cabello
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Editor information

Editors and Affiliations

  1. Dipartimento di Informatica ed Applicazioni, Università di Salerno, 84084, Fisciano, (SA), Italy

    Giuseppe Persiano

  2. Department of Computer Science, The University of Western Ontario, London, Canada

    Roberto Solis-Oba

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© 2005 Springer-Verlag Berlin Heidelberg

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Cabello, S. (2005). Approximation Algorithms for Spreading Points. In: Persiano, G., Solis-Oba, R. (eds) Approximation and Online Algorithms. WAOA 2004. Lecture Notes in Computer Science, vol 3351. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-31833-0_9

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  • DOI: https://doi.org/10.1007/978-3-540-31833-0_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-24574-2

  • Online ISBN: 978-3-540-31833-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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