A Divide and Conquer Approximation Algorithm for Partitioning Rectangles
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Given a rectangle R with area A and a set of areas L={A_1,...,A_n} with ∑_i=1^n A_i = A, we consider the problem of partitioning R into n sub-regions R_1,...,R_n with areas A_1,...,A_n in a way that the total perimeter of all sub-regions is minimized. The goal is to create square-like sub-regions, which are often more desired. We propose an efficient 1.203–approximation algorithm for this problem based on a divide and conquer scheme that runs in 𝒪(n^2) time. For the special case when the aspect ratios of all rectangles are bounded from above by 3, the approximation factor is 2/√(3)≤ 1.1548. We also present a modified version of out algorithm as a heuristic that achieves better average and best run times.
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