Improved algorithm for the widest empty 1-corner corridor

Authors:
Gautam K. Das;Debapriyay Mukhopadhyay;Subhas C. Nandy
Affiliations:
University of New Brunswick, Fredericton, Canada E3B 5A3;Rebaca Technologies Private Limited, Kolkata 700 091, India;Indian Statistical Institute, Kolkata 700108, India
Venue:
Information Processing Letters
Year:
2009

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Abstract

Given a set P of n points on a 2D plane, an empty corridor is an open region bounded by two parallel polygonal chains that does not contain any point of P, and partitions the point-set P into two non-empty parts. An empty corridor is said to be a 1-corner empty corridor if each of the two bounding polygonal chains has exactly one corner point. We present an improved algorithm for computing the widest empty 1-corner corridor. It runs in O(n^3log^2n) time and O(n^2) space. This improves the time complexity of the best known algorithm for the same problem by a factor of nlogn [J.M. Diaz-Banez, M.A. Lopez, J.A. Sellares, On finding a widest empty 1-corner corridor, Information Processing Letters 98 (2006) 199-205].