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Efficient Approximation Algorithms for Multi-label Map Labeling

  • Binhai Zhu
  • C. K. Poon
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1741)

Abstract

In this paper we study two practical variations of the map labeling problem: Given a set distinct sites in the plane, one needs to place at each site: (1) a pair of uniform and non-intersecting squares of maximum possible size, (2) a pair of uniform and non-intersecting circles of maximum possible size. Almost nothing has been done before in this aspect, i.e., multi-label map labeling. We obtain constant-factor approximation algorithms for these problems. We also study bicriteria approximation schemes based on polynomial time approximation sche- mes (PTAS) for these problems

Keywords

Approximation Algorithm Performance Guarantee Polynomial Time Approximation Scheme Polynomial Time Approximation Algorithm Optimal Label 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. BC94.
    D. Beus and D. Crockett. Automated production of 1:24,000 scale quadrangle maps. In Proc. 1994 ASPRS/ACSM Annual Convention and Exposition, volume 1, pages 94–99, 1994.Google Scholar
  2. BO83.
    M. Ben-Or. Lower bounds for algebraic computation trees. In Proc. 15th ACM STOC, pages 80–86, 1983.Google Scholar
  3. CMS93.
    J. Christensen, J. Marks, and S. Shieber. Algorithms for cartographic label placement. In Proc. 1993 ASPRS/ACSM Annual Convention and Exposition, volume 1, pages 75–89, 1993.Google Scholar
  4. CMS95.
    J. Christenson, J. Marks, and S. Shieber. An Empirical Study of Algorithms for Point-Feature Label Placement, ACM Transactions on Graphics,14:203–222, 1995.CrossRefGoogle Scholar
  5. DF92.
    J. Doerschler and H. Freeman. A rule-based system for cartographic name placement. CACM, 35:68–79, 1992.Google Scholar
  6. DLSS.
    A. Datta, II.-P. Lenhof, C. Schwarz, and M. Smid. “Static and dynamic algorithms for k-point clustering problems”, In Proc. 3rd worksh. Algorithms and Data Structures, springer-verlag, LNCS 709, pages 265–276, 1993.Google Scholar
  7. DMMMZ97.
    S. Doddi, M. Marathe, A. Mirzaian, B. Moret and B. Zhu, Map labeling and its generalizations. In Proc. 8th ACM-SIAM Symp on Discrete Algorithms (SODA’97), New Orleans, LA, Pages 148–157, Jan, 1997.Google Scholar
  8. EE94.
    D. Eppstein and J. Erickson. “Iterated nearest neighbors and finding minimal polytopes”, Discrete & Comput. Geom., 11:321–350, 1994.zbMATHCrossRefMathSciNetGoogle Scholar
  9. FW91.
    M. Formann and F. Wagner. A packing problem with applications to lettering of maps. In Proc. 7th Annu. ACM Sympos. Comput. Geom., pages 281–288, 1991.Google Scholar
  10. GJ79.
    M. Garey and D. Johnson. Computers and Intractability: A Guide to the Theory of NP-completeness. Freeman, San Francisco, CA, 1979.zbMATHGoogle Scholar
  11. HM+94.
    H.B. Hunt III, M.V. Marathe, V. Radhakrishnan, S.S. Ravi, D.J. Rosenkrantz and R.E. Stearns, A Unified Approach to Approximation Schemes for NP-and PSPACE-Hard Problems for Geometric Graphs. Proc. Second European Symp. on Algorithms (ESA’94), pages 468–477, 1994.Google Scholar
  12. IL97.
    C. Iturriaga and A. Lubiw. Elastic labels: the two-axis case. In Proc. Graph Drawing’97, pages 181–192, 1997.Google Scholar
  13. Imh75.
    E. Imhof. Positioning names on maps. The American Cartographer, 2:128–144, 1975.CrossRefGoogle Scholar
  14. Jon89.
    C. Jones. Cartographic name placement with Prolog. Proc. IEEE Computer Graphics and Applications, 5:36–47, 1989.CrossRefGoogle Scholar
  15. KSW98.
    M. van Kreveld, T. Strijk and A. Wolff. Point set labeling with sliding labels. In Proc. 14th Annu. ACM Sympos. Comput. Geom., pages 337–346, 1998.Google Scholar
  16. KT97.
    K. Kakoulis and I. Tollis. An algorithm for labeling edges of hierarchical drawings. In Proc. Graph Drawing’97, pages 169–180, 1997.Google Scholar
  17. KT98a.
    K. Kakoulis and I. Tollis. A unified approach to labeling graphical features. Proc. 14th Annu. ACM Sympos. Comput. Geom., pages 347–356, 1998.Google Scholar
  18. KT98.
    K. Kakoulis and I. Tollis. On the multiple label placement problem. In Proc. 10th Canadian Conf. on Comput. Geom., pages 66–67, 1998.Google Scholar
  19. KR92.
    D. Knuth and A. Raghunathan. The problem of compatible representatives. SIAM J. Disc. Math., 5:422–427, 1992.zbMATHCrossRefMathSciNetGoogle Scholar
  20. PS85.
    F.P. Preparata and M.I. Shamos. Computational Geometry: An Introduction. Springer-Verlag, 1985.Google Scholar
  21. PZC98.
    C.K. Poon, B. Zhu and F. Chin, A polynomial time solution for labeling a rectilinear map. Inform. Process. Lett., 65(4):201–207, Feb, 1998.CrossRefMathSciNetGoogle Scholar
  22. Wag94.
    F. Wagner. Approximate map labeling is in (n log n). Inform. Process. Lett., 52:161–165, 1994.zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Binhai Zhu
    • 1
  • C. K. Poon
    • 1
  1. 1.Dept. of Computer ScienceCity University of Hong KongKowloonChina

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