Elastic Labels: The Two-Axis Case

Iturriaga, Claudia and Lubiw, Anna (1998) Elastic Labels: The Two-Axis Case. In: Graph Drawing 5th International Symposium, GD '97, September 18-20, 1997, Rome, Italy , pp. 181-192 (Official URL: http://dx.doi.org/10.1007/3-540-63938-1_61).

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One of the most challenging tasks of cartographic map lettering is the optimal placement of region information on a map. We propose as an approach to this task the elastic labeling problem, in which we are given a set of elastic rectangles as labels, each associated with a point in the plane. An elastic rectangle has a specified area but its width and high may vary. The problem then is to choose the height and width of each label, and the corner of the label to place at the associated point, so that no two labels overlap. This problem is known to be NP-hard even when there is no elasticity (just because of the choice of the corners). We show that the problem remains NP-hard when we have elasticity but no choice about which corner of the label to use - we call this the one-corner elastic labeling problem. We give a polynomial time algorithm for the special case of the one-corner elastic labeling problem in which the points lie on the positive x and y axes and the lables lie in the first quadrant. We call this the two-axis labeling problem.

Item Type:Conference Paper
Additional Information:10.1007/3-540-63938-1_61
Classifications:G Algorithms and Complexity > G.630 Labeling
ID Code:76

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J. Christensen, J. Marks, and S. Shieber. An empirical study of algorithms for point feature label placement. ACM Transactions on Graphics. (1995) 14(3), 203-232.

J.S. Doerschler and H. Freeman. A rule-based system for dense-map name placement. Communications of the Association of Computing Machinery. (1992) 35(1), 68-79.

M. Formann and F. Wagner. A packing problem with applications in lettering of maps. Proceedings of the 7th ACM Symposium on Computational Geometry. (1991) 281-288.

E. Imhof. Positioning names on maps. The American Cartographer. (1975) 2,128-144.

C. Iturriaga and A. Lubiw. NP-hardness of some map labeling problems. Technical Report CS-97-18. University of Waterloo (1997).

C. Iturriaga. Ph.D. Thesis, in progress. University of Waterloo.

T. Kato and H. Imai. The NP-completeness of the character placement problem of 2 or 3 degrees of freedom. Record of Joint Conference of Electrical and Electronic engineers in Kyushu. (1988), 1138. In Japanese.

D. Knuth and A. Raghunathan. The problem of compatible representatives. SIAM Disc. Math. (1992)5 (3), 422-427.

J.Matks and S. Shieber. The computational complexity of cartographic label placement. Technical Report CRCT-05-91. Harvard University (1991).

F. Wagner and A. Wolff. A practical map labeling algorithm. Computational Geometry: Theory and Applications. (1997) 387-404.

P. Yoeli. The logic of automated map lettering. The Cartographic Journal. (1972) 9, 99-108.