Covering points by disjoint boxes with outliers
Author(s)Ahn, Hee-Kap; Bae, Sang Won; Demaine, Erik D.; Demaine, Martin L.; Kim, Sang-Sub; Korman, Matias; Reinbacher, Iris; Son, Wanbin; ... Show more Show less
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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 at least n−k points. In this paper, we consider the boxes to be either squares or rectangles, and we want to minimize the area of the largest box. For general p we show that the problem is NP-hard for both squares and rectangles. For a small, fixed number p, we give algorithms that find the solution in the following running times: For squares we have O(n+klogk) time for p=1, and O(nlogn+k[superscript p]log[superscript p]k) time for p=2,3. For rectangles we get O(n+k[superscript 3]) for p=1 and O(nlogn+k[superscript 2+p]log[superscript p−1]k) time for p=2,3. In all cases, our algorithms use O(n) space.
DepartmentMassachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory; Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Ahn, Hee-Kap, Sang Won Bae, Erik D. Demaine, Martin L. Demaine, Sang-Sub Kim, Matias Korman, Iris Reinbacher, and Wanbin Son. “Covering Points by Disjoint Boxes with Outliers.” Computational Geometry 44, no. 3 (April 2011): 178–90.
Author's final manuscript