FAW 2009: Frontiers in Algorithmics pp 132-140

Square and Rectangle Covering with Outliers

• Hee-Kap Ahn
• Sang Won Bae
• Sang-Sub Kim
• Matias Korman
• Iris Reinbacher
• Wanbin Son
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5598)

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 + klogk) time for p = 1, and in O(nlogn + kplogpk) time for p = 2,3. For rectangles we have running times of O(n + k3) for p = 1 and O(nlogn + k2 + plogp − 1k) time for p = 2,3. In all cases, our algorithms use O(n) space.

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Authors and Affiliations

• Hee-Kap Ahn
• 1
• Sang Won Bae
• 1
• Sang-Sub Kim
• 1
• Matias Korman
• 2
• Iris Reinbacher
• 1
• Wanbin Son
• 1
1. 1.Department of Computer Science and EngineeringPOSTECHSouth Korea
2. 2.Graduate School of Information ScienceTohoku UniversityJapan