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2005
Springer

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

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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.
Sergio Cabello, Panos Giannopoulos, Christian Knau
Added 27 Jun 2010
Updated 27 Jun 2010
Type Conference
Year 2005
Where ESA
Authors Sergio Cabello, Panos Giannopoulos, Christian Knauer, Günter Rote
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