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The transportation problem in the plane - how to move a set of objects fromone set of points to another set of points in the cheapest way - is a very oldproblem going back several hundreds of years. In recent years the solution ofthe problem has found applications in the analysis of digital images whensearching for similarities and discrepancies between images. The main drawback,however, is the long computation time for finding the solution.  In this paper we present some new results by which the time for solving thetransportation problem in the plane can be reduced substantially. Ascost-function we choose a distance-function between points in the plane. Weconsider both the case when the distance-function is equal to the ordinaryEuclidean distance, as well as the case when the distance-function is equal tothe square of the Euclidean distance. This latter distance-function has theadvantage that it is integer-valued if the coordinates of the points in theplane are integers.

Improving the primal-dual algorithm for the transportation problem in the plane