A bottleneck plane perfect matching of a set of n points in R 2 is defined to be a perfect non-crossing matching that minimizes the length of the longest edge; the length of this longest edge is known as bottleneck. The problem of computing a bottleneck plane perfect matching has been proved to be NP-hard. We present an algorithm that computes a bottleneck plane matching of size at least n 5 in O(n log 2 n)-time. Then we extend our idea toward an O(n log n)-time approximation algorithm which computes a plane matching of size at least 2n 5 whose edges have length at most √ 2 + √ 3 times the bottleneck.
In REF , the authors showed how to compute a plane matching of size at least n/5, whose edges have length at most λ * in O(n log 2 n) time, and a plane matching of size at least 2n/5, whose edges have length at most (
Approximating the Bottleneck Plane Perfect Matching of a Point Set
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Mathematics Computer Science