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Location of the largest empty rectangle among arbitrary obstacles

  • Subhas C. Nandy
  • Arani Sinha
  • Bhargab B. Bhattacharya
Algorithms
Part of the Lecture Notes in Computer Science book series (LNCS, volume 880)

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(nlog2n) 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 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • Subhas C. Nandy
    • 1
  • Arani Sinha
    • 1
  • Bhargab B. Bhattacharya
    • 1
  1. 1.Indian Statistical InstituteCalcuttaIndia

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