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arXiv · 1502.03847

A Constant Factor Approximation for Orthogonal Order Preserving Layout Adjustment

Sayan Bandyapadhyay·Santanu Bhowmick·Kasturi Varadarajan
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Abstract

Given an initial placement of a set of rectangles in the plane, we consider the problem of finding a disjoint placement of the rectangles that minimizes the area of the bounding box and preserves the orthogonal order i.e.\ maintains the sorted ordering of the rectangle centers along both $x$-axis and $y$-axis with respect to the initial placement. This problem is known as Layout Adjustment for Disjoint Rectangles(LADR). It was known that LADR is $\mathbb{NP}$-hard, but only heuristics were known for it. We show that a certain decision version of LADR is $\mathbb{APX}$-hard, and give a constant factor approximation for LADR.

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Sayan Bandyapadhyay, Santanu Bhowmick, Kasturi Varadarajan. 2015-02-12. A Constant Factor Approximation for Orthogonal Order Preserving Layout Adjustment. https://arxiv.org/abs/1502.03847

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