Finding a widest empty 1-corner corridor

Given a set of n points in the plane, we consider the problem of computing a widest empty 1-corner corridor. We star giving a characterization of the 1-corner corridors that we call locally widest. Our approach to finding a widest empty 1-corner corridor consists of identifying a set of 1-corner corridors locally widest, that is guaranteed to contain a solution. We describe an algorithm that solves the problem in O(n4 log n) time and O(n) space.