Computational Experience with an Approximation Algorithm on Large-Scale Euclidean Matching Instances

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We consider a 2-approximation algorithm for Euclidean minimum-cost perfect matching instances proposed by the authors in a previous paper. We present computational results for both random and real-world instances having between 1,000 and 131,072 vertices. The results indicate that our algorithm generates a matching within 2% of optimal in most cases. In over 1,400 experiments, the algorithm was never more than 4% from optimal. For the purposes of the study, we give a new implementation of the algorithm that uses linear space instead of quadratic space, and appears to run faster in practice.