Extensions of the Maximum Bichromatic Separating Rectangle Problem
share
In this paper, we study two extensions of the maximum bichromatic separating rectangle (MBSR) problem introduced in <cit.>. One of the extensions, introduced in <cit.>, is called MBSR with outliers or MBSR-O, and is a more general version of the MBSR problem in which the optimal rectangle is allowed to contain up to k outliers, where k is given as part of the input. For MBSR-O, we improve the previous known running time bounds of O(k^7 m log m + n) to O(k^3 m + m log m + n). The other extension is called MBSR among circles or MBSR-C and asks for the largest axis-aligned rectangle separating red points from blue unit circles. For MBSR-C, we provide an algorithm that runs in O(m^2 + n) time.
READ FULL TEXT