Matching Point Sets with Respect to the Earth Mover's Distance

Let A and B be two sets of m resp. n weighted points in the plane, with m ≤ n. We present (1 + ) and (2+ )-approximation algorithms for the minimum Euclidean Earth Mover’s Distance between A and B under translations and rigid motions respectively. In the general case where the sets have unequal total weights the algorithms run in O((n3 m/ 4 ) log2 (n/ )) time for translations and O((n4 m2 / 4 ) log2 (n/ )) time for rigid motions. When the sets have equal total weights, the respective running times decrease to O((n2 / 4 ) log2 (n/ )) and O((n3 m/ 4 ) log2 (n/ )). We also show how to compute a (1 + ) and (2 + )approximation of the minimum cost Euclidean bipartite matching under translations and rigid motions in O((n3/2 / 7/2 ) log5 n) and O((n/ )7/2 log5 n) time respectively.

• Type: Conference
• Year: 2005
• Where: ESA
• Authors: Sergio Cabello, Panos Giannopoulos, Christian Knauer, Günter Rote
• Keywords: ESA 2005, Minimum Euclidean Earth, Rigid Motions, Total Weights