Approximation algorithm for the largest area convex hull of same size non-overlapping axis-aligned squares

Authors:
Wenqi Ju;Jun Luo
Affiliations:
Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, China and Institute of Computing Technology, Chinese Academy of Sciences, China;Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, China
Venue:
FAW'10 Proceedings of the 4th international conference on Frontiers in algorithmics
Year:
2010

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Abstract

Given a set of n equal size and non-overlapping axis-aligned squares, we need to choose exactly one point in each square to make the area of a convex hull of the resulting point set as large as possible. Previous algorithm [10] on this problem gives an optimal algorithm with O(n3) running time. In this paper, we propose an approximation algorithm which runs in O(n log n) time and gives a convex hull with area larger than the area of the optimal convex hull minus the area of one square.