On Random Line Segments in the Unit Square
نویسنده
چکیده
I. INTRODUCTION Let Q = [0, 1] × [0, 1] denote the unit square and let L n be a set of n line segments in Q. Two line segments are said to be crossing if they intersect at any point. A subset of line segments is called non-crossing if no two segments in the subset are crossing. Consider the scenario where the endpoints of the n line segments are randomly distributed, independently and uniformly, in Q. Define N (L n) to be the size of the largest non-crossing subset of segments. Formally:
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