Maximum Area Rectangle Separating Red and Blue Points

Bogdan Armaselu; Ovidiu Daescu

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arXiv · 1706.03268

Maximum Area Rectangle Separating Red and Blue Points

Bogdan Armaselu·Ovidiu Daescu

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Abstract

Given a set R of n red points and a set B of m blue points, we study the problem of finding a rectangle that contains all the red points, the minimum number of blue points and has the largest area. We call such rectangle a maximum separating rectangle. We address the planar, axis-aligned (2D) version, and present an O(mlogm+n) time, O(m+n) space algorithm. The running time reduces to O(m + n) if the points are pre-sorted by one of the coordinates. We further prove that our algorithm is optimal in the decision model of computation.

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BibTeX RIS

Bogdan Armaselu, Ovidiu Daescu. 2017-06-10. Maximum Area Rectangle Separating Red and Blue Points. https://arxiv.org/abs/1706.03268

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