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Map Labeling with Circles: Author: jiang, Minghui; Date: 2005-05-15; Program: Computer Science; Abstract: We study two geometric optimization problems motivated by cartographic applications: Map Labeling with Uniform Circles (MLUC) and Map Labeling with Uniform Circle Pairs (MLUCP). We show that the decision problems of both MLUC and MLUCP are NP-hard, and that the related optimization problems for maximizing the label sizes are NP-hard to approximate within factor 1.0349. We design approximation algorithms with constant performance guarantees for the two problems: for MLUC, we present a (3 + ε)-approximation and a (2.98 + ε)-approximation; for MLUCP, a (1.5+�µ...; Download File | View full details