A Combinatorial Framework for Map Labeling

Wagner, Frank and Wolff, Alexander (1998) A Combinatorial Framework for Map Labeling. In: Graph Drawing 6th International Symposium, GD’ 98, August 13-15, 1998, Montréal, Canada , pp. 316-321 (Official URL: http://dx.doi.org/10.1007/3-540-37623-2_24).

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Abstract

The general map labeling problem consists in labeling a set of sites (points, lines, regions) given a set of candidates (rectangles, circles, ellipses, irregularly shaped labels) for each site. A map can be a classical cartographical map, a diagram, a graph or any other figure that needs to be labeled. A labeling is either a complete set of non-conflicting candidates, one per site, or a subset of maximum cardinality. Finding such a labeling is NP-hard. We present a combinatorial framework to attack the problem in its full generality. The key idea is to separate the geometric from the combinatorial part of the problem. The latter is captured by the conflict graph of the candidates and by rules which successively simplify this graph towards a near-optimal solution. We exemplify this framework at the problem of labeling point sets with axis-parallel rectangles as candidates, four per point. We do this such that it becomes clear how our concept can be applied to other cases. We study competing algorithms and do a thorough empirical comparison. The new algorithm we suggest is fast, simple and effective.

Item Type:Conference Paper
Additional Information:10.1007/3-540-37623-2_24
Classifications:G Algorithms and Complexity > G.630 Labeling
ID Code:339

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References

P. Agarwal, M. van Kreveld, and S. Suri. Label placement by maximum independent set in rectangles. In Proceedings of the 9th Canadian Conference on Computational Geometry, pages 233-238, 1997.

J. Christensen, S. Friedman, J. Marks, and S. Shieber. Empirical testing of algorithms for variable-sized label placement. In proc. 13th Annu. ACM Symp. Comput. Geom., pages 415-417,1997.

J. Christensen, J. Marks, and S. Shieber. An empirical study of algorithms for Point Feature Label Placement. ACM Trans. on Graphics, 14(3):203-232, July 1995.

Srinivas Doddi, Madhav V. Marathe, Andy Mirzaian, Bernard M.E. Moret, and Binhai Zhu. Map labeling and its generalizations. In Proceedings of the 8th ACM-SIAM Symposium on Discrete Algorithms, pages 148-157, 1997.

Robert J. Fowler, Michael S. Paterson, and Steven L. Tanimoto. Optimal packing and covering in the plane are NP-complete. Inform. Process. Lett. , 12(3):133-137, 1981.

M. Formann, F. Wagner. A packing problem with applications to lettering of maps. Proc. of 7th Annual Symp. on Comp. Geom., pages 281-288, 1991.

Eugene C. Freuder and Richard J. Wallace. Partial constraint satisfaction. Jour. Artifical Intelligence, 58:21-70, 1992.

Stephen A. Hirsch. An algorithm for automatic name placement around point data. The American Cartographer, 9(1):5-17, 1982.

Michael B. Jampel. Over-constrained systems in CLP ans CSP. PhD thesis, Dept. of Comp. Sci. City University, London, sept 1996.

Michael Jampel, Eugene Freuder, and Michael Maher, editors. Over-constrained systems. Number 1106 in LNCS. Springer, August 1996.

Donald E. Knuth and Arvind Raghunathan. The problem of compatible representatives. SIAM J. Diskr. Math., 5(3):422-427, 1992.

K.G. Kakoulis and I.G. Tollis. A unified approach to labeling graphical features. In Proc. 14th Annu. ACM Sympos. Comput. Geom., pages 347-356, June 1998.

Alan K. Marckworth and Eugen C. Freuder. The complexity of some polynomial network consistency algorithms for constraint satisfaction problems. Jour. Artifical Intelligence, 25:65-74, 1985.

Thomas Schiex, Helene Fargier, and Gerard Verfaillie. Valued constraint satisfaction problems: Hard and easy problems. In Proc. International Joint Conference on AI, aug 1995.

Marc van Kreveld, Tycho Strijk, and Alexander Wollf. Point set labeling with sliding labels. Proc. of 14th Annual Symp. on Comp. Geom., pages 337-346, June 1998.

Frank Wagner. Approximate map labeling is in \Omega(nlogn). Information Processing Letters, 52(3):161-165, 1994.

Frank Wagner and Alexander Wollf. A practical map labeling algorithm. Computational Geometry: Theory and Applications, 7:387-404, 1997.