Abstract
We study the problem of computing Euclidean minimum weight matching which investigates the minimum weight perfect matching in a complete geometric graph on a set of 2n points in the plane. We propose a simple randomized approximation algorithm based on the geometrical aspect of the problem with O(n) expected time. The proposed algorithm computes a matching within at most 3 factors of the optimal solution. We also do some experimental tests to evaluate the performance of the proposed algorithm which indicate the efficiency of the proposed algorithm in finding the approximate matching in the practice.
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