On Bipartite Matching under the RMS Distance

Given two sets A and B of n points each in R2 , 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+ ) time, for any > 0, and an -approximation in time O((n/)3/2 log6 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 /5/2 ) log6 n) time whose cost is within (1 + ) factor of the optimal one.

• Type: Conference
• Year: 2006
• Where: CCCG
• Authors: Jeff M. Phillips, Pankaj K. Agarwal
• Keywords: CCCG 2006, CCCG 2007, Compute, Optimal Matching, Root Mean Square