Square and Rectangle Covering with Outliers

Authors:
Hee-Kap Ahn;Sang Won Bae;Sang-Sub Kim;Matias Korman;Iris Reinbacher;Wanbin Son
Affiliations:
Department of Computer Science and Engineering, POSTECH, South Korea;Department of Computer Science and Engineering, POSTECH, South Korea;Department of Computer Science and Engineering, POSTECH, South Korea;Graduate School of Information Science, Tohoku University, Japan;Department of Computer Science and Engineering, POSTECH, South Korea;Department of Computer Science and Engineering, POSTECH, South Korea
Venue:
FAW '09 Proceedings of the 3d International Workshop on Frontiers in Algorithmics
Year:
2009

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Abstract

For a set of n points in the plane, we consider the axis---aligned (p ,k )-Box Covering problem: Find p axis-aligned, pairwise disjoint boxes that together contain exactly n *** k points. Here, our boxes are either squares or rectangles, and we want to minimize the area of the largest box. For squares, we present algorithms that find the solution in O (n + k logk ) time for p = 1, and in O (n logn + k p log p k ) time for p = 2,3. For rectangles we have running times of O (n + k 3) for p = 1 and O (n logn + k 2 + p log p *** 1 k ) time for p = 2,3. In all cases, our algorithms use O (n ) space.