Abstract
We study the problem of finding a minimum weight complete matching in the complete graph on a set V ofn points ink-dimensional space. The points are the vertices of the graph and the weight of an edge between any two points is the distance between the points under someL q,-metric. We give anO((2c q )1.5k ɛ−1.5k (α(n, n))0.5 n 1.5(logn)2.5) algorithm for finding an almost minimum weight complete matching in such a graph, wherec q =6k 1/q for theL q -metric, α is the inverse Ackermann function, and ɛ ≤ 1. The weight of the complete matching obtained by our algorithm is guaranteed to be at most (1 + ɛ) times the weight of a minimum weight complete matching.
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