On finding a widest empty 1-corner corridor

  • Authors:
  • J. M. Díaz-Báòez;M. A. López;J. A. Sellarès

  • Affiliations:
  • Universidad de Sevilla, Spain;University of Denver, USA;Universitat de Girona, Spain

  • Venue:
  • Information Processing Letters
  • Year:
  • 2006

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Abstract

A 1-corner corridor through a set S of points is an open subset of CH(S) containing no points from S and bounded by a pair of parallel polygonal lines each of which contains two segments. Given a set of n points in the plane, we consider the problem of computing a widest empty 1-corner corridor. We describe an algorithm that solves the problem in O(n^4logn) time and O(n) space. We also present an approximation algorithm that computes in O(nlogn@e^1^/^2+n^2@e) time a solution with width at least a fraction (1-@e) of the optimal, for any small enough @e0.