Efficient minimum cost matching and transportation using the quadrangle inequality

We present efficient algorithms for finding a minimum cost perfect matching, and forsolving the transportation problem in bipartite graphs, G = (Sinks [ Sources; Sinks 2Sources), wherejSinksj= n, jSourcesj= m, n m, and the cost function obeys thequadrangle inequality. First, we assume that all the sink points and all the source points lieon a curve that is homeomorphic to either a line or a circle and the cost function is given bythe Euclidean distance along the curve. We...