# Location of the largest empty rectangle among arbitrary obstacles

## Abstract

This paper outlines the following generalization of the classical maximal-empty-rectangle (MER) problem: given *n* arbitrarily-oriented non-intersecting line segments of finite length on a rectangular floor, locate an empty *isothetic* rectangle of maximum area. Thus, the earlier restriction on isotheticity of the obstacles is relaxed. Based on the wellknown technique of matrix searching, a novel algorithm of time complexity *O(n*log^{2}*n*) and space complexity *O(n)*, is proposed. Next, the technique is extended to handle the following two related open problems: locating the largest isothetic MER (i) inside an arbitrary simple polygon and (ii) amidst a set of arbitrary polygonal obstacles.

## Keywords

Computational geometry algorithms matrix search complexity## Preview

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## References

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