New bounds on map labeling with circular labels

Abstract

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 + ε)-approximation for MLUC, improving previous factor 3.0+ε a (1.491+ε)-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). © Springer-Verlag 2004.