Abstract
In this paper we present approximation algorithm for the following NP-hard map labeling problem: Given a set S of n distinct sites in the plane, one needs to place at each site a uniform square of maximum possible size such that all the squares are along the same direction. This generalizes the classical problem of labeling points with axis-parallel squares and restricts the most general version where the squares can have different orientations. We obtain factor-4 and factor-\(5\sqrt 2 \) approximation algorithms for this problem. These algorithms also work for two generalized versions of the problem. We also revisit the problem of labeling each point with maximum uniform axis-parallel square pairs and improve the previous approximation factor of 4 to 3.
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Zhu, B., Qin, Z. New Approximation Algorithms for Map Labeling with Sliding Labels. Journal of Combinatorial Optimization 6, 99–110 (2002). https://doi.org/10.1023/A:1013326409918
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DOI: https://doi.org/10.1023/A:1013326409918