Theory and application of width bounded geometric separator

Authors:
Bin Fu
Affiliations:
Dept. of Computer Science, University of New Orleans, LA
Venue:
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
Year:
2006

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Abstract

We introduce the notion of the width bounded geometric separator and develop the techniques for the existence of the width bounded separator in any d-dimensional Euclidean space. The separator is applied in obtaining $2^{O(\sqrt{n})}$ time exact algorithms for a class of NP-complete geometric problems, whose previous algorithms take $n^{O(\sqrt{n})}$ time[2][5][1]. One of those problems is the well known disk covering problem, which seeks to determine the minimal number of fixed size disks to cover n points on a plane[10]. They also include some NP-hard problems on disk graphs such as the maximum independent set problem, the vertex cover problem, and the minimum dominating set problem.