On the rectangular subset closure of point sets

Authors:
Stefan Porschen
Affiliations:
Institut für Informatik, Universität zu Köln, Köln, Germany
Venue:
ICCSA'05 Proceedings of the 2005 international conference on Computational Science and its Applications - Volume Part I
Year:
2005

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Abstract

Many applications like picture processing, data compression or pattern recognition require a covering of a set of points most often located in the (discrete) plane by rectangles due to some cost constraints. In this paper we introduce and study the concept of the rectangular subset closure of a point set M in the (discrete) plane which is aimed to provide some insight into the rectangular combinatorial structure underlying such a covering problem. We show that the rectangular subset closure of a set M is of size O(|M|2) and that it can be computed in time O(|M|2). The concepts and results are also generalized to the d-dimensional case.