论文信息 - A new bound for map labeling with uniform circle pairs

A new bound for map labeling with uniform circle pairs

Given a planar point set, we wish to label the points with uniform circular labels such that each input point lies on the boundary of two labels, none of the interiors of the labels intersect, and the size of the labels is maximized. This problem is known as map-labeling with uniform circular pairs (MLUCP) and has been shown to be NP-hard. In this paper, we give an O(nlogn) time, O(n) space algorithm that computes a labeling, such that the diameter of the circular labels in an optimum solution is no more than (1+33)/4≈1.686 times the diameter of the labels computed by our algorithm.

J. Mark Keil | Michael J. Spriggs

[1] Frank Wagner,et al. A packing problem with applications to lettering of maps , 1991, SCG '91.

[2] Alexander Wolff,et al. A Better Lower Bound for Two-Circle Point Labeling , 2000, ISAAC.

[3] Binhai Zhu,et al. Efficient Approximation Algorithms for Multi-label Map Labeling , 1999, ISAAC.

[4] Bernard Chazelle,et al. A Functional Approach to Data Structures and Its Use in Multidimensional Searching , 1988, SIAM J. Comput..

[5] Madhav V. Marathe,et al. Point set labeling with specified positions , 1999, SCG '00.

[6] Leonidas J. Guibas,et al. Primitives for the manipulation of general subdivisions and the computation of Voronoi diagrams , 1983, STOC.

[7] Ioannis G. Tollis,et al. A unified approach to labeling graphical features , 1998, SCG '98.

[8] Leonidas J. Guibas,et al. Primitives for the manipulation of general subdivisions and the computation of Voronoi diagrams , 1983, STOC.

[9] Alexander Wolff,et al. New Algorithms for Two-Label Point Labeling , 2000, ESA.