An efficient and effective approximation algorithm for the Map Labeling Problem

  • Frank Wagner
  • Alexander Wolff
Session 7. Chair: Michael Goemans
Part of the Lecture Notes in Computer Science book series (LNCS, volume 979)

Abstract

The Map Labeling Problem is a classical problem of cartography. There is an approximation algorithm A which is theoretically optimal: A has optimal running time and guarantees a label size of 50 percent of the maximum. Unfortunately A is useless in practice as it typically produces results that are intolerably far off the optimal size. On the other hand there is a heuristic with good practical results, which is used in real applications.

Recently a hybrid algorithm was suggested that first runs A and then uses its result to control the heuristic.

In this paper we integrate the two parts of the hybrid method into an efficient and effective approximation algorithm. In addition we include a strategy to improve the empirical quality of the results significantly. The resulting algorithm B
  • guarantees optimal approximation quality and runtime behaviour, and

  • yields results closer to the optimum than the best heuristic known so far.

The sample data used in the experimental evaluation consists of three different classes of random problems and a selection of problems arising in the production of groundwater quality maps by the authorities of the City of München.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [AIK89]
    H. Aonuma, H. Imai, Y. Kambayashi, A visual system of placing characters appropriatly in multimedia map databases, Proceedings of the IFIP TC 2/WG 2.6 Working Conference on Visual Database Systems, North Holland (1989) 525–546Google Scholar
  2. [EIS76]
    S. Even, A. Itai, A. Shamir, On the complexity of Timetable and Multicommodity Flow Problems, SIAM Journal on Computing 5 (1976) 691–703CrossRefGoogle Scholar
  3. [F92]
    M. Formann, Algorithms for Geometric Packing and Scaling Problems, Dissertation, Fachbereich Mathematik und Informatik, Freie Universität Berlin (1992)Google Scholar
  4. [FW91]
    M. Formann, F. Wagner, A Packing Problem with Applications to Lettering of Maps, Proceedings of the 7th Annual ACM Symposium on Computational Geometry (1991) 281–288Google Scholar
  5. [FW]
    M. Formann, F. Wagner, An efficient solution to Knuth's METAFONT labeling problem, Manuscript (1993)Google Scholar
  6. [175]
    E. Imhof, Positioning Names on Maps, The American Cartographer 2 (1975) 128–144Google Scholar
  7. [KR92]
    D. E. Knuth And A. Raghunathan, The Problem of Compatible Representatives, SIAM Journal on Discrete Mathematics 5 (1992) 422–427CrossRefGoogle Scholar
  8. [MN95]
    K. Mehlhorn and S. Näher, LEDA: a platform for combinatorial and geometric computing, Communications of the ACM 38 (1995) 96–102CrossRefGoogle Scholar
  9. [IA86]
    H. Imai, T. Asano, Efficient Algorithms for Geometric Graph Search Problems, SIAM J. Comput. 15 (1986) 478–494Google Scholar
  10. [KMPS93]
    L. Kučera, K. Mehlhorn, B. Preis, E. Schwarzenecker, Exact Algorithms for a Geometric Packing Problem, Proceedings of the 10th Annual Symposium on Theoretical Aspects of Computer Science, Lecture Notes in Computer Science 665 (1993) 317–322Google Scholar
  11. [W94]
    F. WagnerApproximate Map Labeling is in Ω(n log n), Information Processing Letters 52 (1994) 161–165Google Scholar
  12. [WW95]
    F. Wagner, A. Wolff Map Labeling Heuristics: Provably Good and practically Useful, to appear in: Proceedings of the 11th Annual ACM Symposium on Computational Geometry (1995)Google Scholar
  13. [WKA94]
    G. Weber, L. Knipping, H. Alt, An Application of Point Pattern Matching in Astronautics, Journal of Symbolic Computation 17 (1994) 321–340Google Scholar

Copyright information

© Springer-Verlag 1995

Authors and Affiliations

  • Frank Wagner
    • 1
  • Alexander Wolff
    • 1
  1. 1.Freie Universität BerlinGermany

Personalised recommendations