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Abstract: For a set of n points in the plane, we consider the axis-aligned p,k-BoxCovering problem: Find p axis-aligned, pairwise-disjoint boxes that togethercontain n-k points. In this paper, we consider the boxes to be either squaresor rectangles, and we want to minimize the area of the largest box. For generalp we show that the problem is NP-hard for both squares and rectangles. For asmall, fixed number p, we give algorithms that find the solution in thefollowing running times:For squares we have On+k log k time for p=1, and On log n+k^p log^p k timefor p = 2,3. For rectangles we get On + k^3 for p = 1 and On log n+k^{2+p}log^{p-1} k time for p = 2,3.In all cases, our algorithms use On space.



Author: Hee-Kap Ahn, Sang Won Bae, Erik D. Demaine, Martin L. Demaine, Sang-Sub Kim, Matias Korman, Iris Reinbacher, Wanbin Son

Source: https://arxiv.org/







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