论文信息 - New Bounds on Map Labeling with Circular Labels

New Bounds on Map Labeling with Circular Labels

We present new approximation algorithms for the NP-hard problems of labeling points with maximum-size uniform circles and circle pairs (MLUC and MLUCP) Our algorithms build on the important concept of maximal feasible region and new algorithmic techniques We obtain several results: a (2.98 + e)-approximation for MLUC, improving previous factor 3.0 + e; a (1.491 + e)-approximation for MLUCP, improving previous factor 1.5; and the first non-trivial lower bound 1.0349 for both MLUC and MLUCP, improving previous lower bound 1+O(1/n).

Sergey Bereg | Binhai Zhu | Minghui Jiang | Zhongping Qin

[1] N. S. Barnett,et al. Private communication , 1969 .

[2] J. Mark Keil,et al. A new bound for map labeling with uniform circle pairs , 2002, Inf. Process. Lett..

[3] Madhav V. Marathe,et al. Map labeling and its generalizations , 1997, SODA '97.

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

[5] Donald E. Knuth,et al. The Problem of Compatible Representatives , 1992, SIAM J. Discret. Math..

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

[7] David Lichtenstein,et al. Planar Formulae and Their Uses , 1982, SIAM J. Comput..

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

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

[10] Binhai Zhu,et al. A simple factor-3 approximation for labeling points with circles , 2003, Inf. Process. Lett..

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

[12] Alexander Wolff,et al. Labeling Points with Circles , 2001, Int. J. Comput. Geom. Appl..