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
Binhai Zhu’s research is supported by City University of Hong Kong, Laurentian University, NSERC of Canada and Hong Kong RGC CERG grant CityU110399E.
C.K. Poon’s research is supported by Hong Kong RGC Competitive Earmarked Research Grant 9040314.
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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.
M. Ben-Or. Lower bounds for algebraic computation trees. In Proc. 15th ACM STOC, pages 80–86, 1983.
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.
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.
J. Doerschler and H. Freeman. A rule-based system for cartographic name placement. CACM, 35:68–79, 1992.
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.
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.
D. Eppstein and J. Erickson. “Iterated nearest neighbors and finding minimal polytopes”, Discrete & Comput. Geom., 11:321–350, 1994.
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.
M. Garey and D. Johnson. Computers and Intractability: A Guide to the Theory of NP-completeness. Freeman, San Francisco, CA, 1979.
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.
C. Iturriaga and A. Lubiw. Elastic labels: the two-axis case. In Proc. Graph Drawing’97, pages 181–192, 1997.
E. Imhof. Positioning names on maps. The American Cartographer, 2:128–144, 1975.
C. Jones. Cartographic name placement with Prolog. Proc. IEEE Computer Graphics and Applications, 5:36–47, 1989.
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.
K. Kakoulis and I. Tollis. An algorithm for labeling edges of hierarchical drawings. In Proc. Graph Drawing’97, pages 169–180, 1997.
K. Kakoulis and I. Tollis. A unified approach to labeling graphical features. Proc. 14th Annu. ACM Sympos. Comput. Geom., pages 347–356, 1998.
K. Kakoulis and I. Tollis. On the multiple label placement problem. In Proc. 10th Canadian Conf. on Comput. Geom., pages 66–67, 1998.
D. Knuth and A. Raghunathan. The problem of compatible representatives. SIAM J. Disc. Math., 5:422–427, 1992.
F.P. Preparata and M.I. Shamos. Computational Geometry: An Introduction. Springer-Verlag, 1985.
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.
F. Wagner. Approximate map labeling is in (n log n). Inform. Process. Lett., 52:161–165, 1994.
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Zhu, B., Poon, C.K. (1999). Efficient Approximation Algorithms for Multi-label Map Labeling. In: Algorithms and Computation. ISAAC 1999. Lecture Notes in Computer Science, vol 1741. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46632-0_15
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DOI: https://doi.org/10.1007/3-540-46632-0_15
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