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Efficient Minimum Cost Matching and Transportation Using Quadrangle Inequality

dc.contributor.authorAggarwal, Aloken_US
dc.contributor.authorBar-Noy, Amotzen_US
dc.contributor.authorKhuller, Samiren_US
dc.contributor.authorKravets, Dinaen_US
dc.contributor.authorSchieber, Baruchen_US
dc.description.abstractWe present efficient algorithms for finding a minimum cost perfect matching, and for solving the transportation problem in bipartite graphs, G=(\Red\cup \Blue, \Red\times \Blue), where |\Red|=n, |\Blue|=m, n\le m, and the cost function obeys the quadrangle inequality. First, we assume that all the \red\ points and all the \blue\ points lie on a curve that is homeomorphic to either a line or a circle and the cost function is given by the Euclidean distance along the curve. We present a linear time algorithm for the matching problem that is simpler than the algorithm of \cite{kl75}. We generalize our method to solve the corresponding transportation problem in O((m+n) \log (m+n)) time, improving on the best previously known algorithm of \cite{kl75}. Next, we present an O(n\log m)-time algorithm for minimum cost matching when the cost array is a bitonic Monge array. An example of this is when the \red\ points lie on one straight line and the \blue\ points lie on another straight line Finally, we provide a weakly polynomial algorithm for the transportation problem in which the associated cost array is a bitonic Monge array. Our algorithm for this problem runs in O(m \log(\sum_{j=1}^m \sj_j)) time, where \di_i is the demand at the ith sink, \sj_j is the supply available at the jth source, and \sum_{i=1}^n \di_i \le \sum_{j=1}^m \sj_j. (Also cross-referenced as UMIACS-TR-93-140)en_US
dc.format.extent414595 bytes
dc.relation.ispartofseriesUM Computer Science Department; CS-TR-3199en_US
dc.relation.ispartofseriesUMIACS; UMIACS-TR-93-140en_US
dc.titleEfficient Minimum Cost Matching and Transportation Using Quadrangle Inequalityen_US
dc.typeTechnical Reporten_US
dc.relation.isAvailableAtDigital Repository at the University of Marylanden_US
dc.relation.isAvailableAtUniversity of Maryland (College Park, Md.)en_US
dc.relation.isAvailableAtTech Reports in Computer Science and Engineeringen_US
dc.relation.isAvailableAtUMIACS Technical Reportsen_US

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