On Bipartite Matching under the RMS Distance
نویسندگان
چکیده
Given two sets A and B of n points each in R, we study the problem of computing a matching between A and B that minimizes the root mean square (rms) distance of matched pairs. We can compute an optimal matching in O(n2+δ) time, for any δ > 0, and an ε-approximation in time O((n/ε)3/2 log n). If the set B is allowed to move rigidly to minimize the rms distance, we can compute a rigid motion of B and a matching in O((n4/ε5/2) log n) time whose cost is within (1 + ε) factor of the optimal one.
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