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Given two sets S and T, a limited-capacity many-to-many matching (LCMM)between S and T matches each element p in S (resp. T) to at least 1 and at mostCap(p) elements in T (resp. S), where the function Cap:S\cup T-> Z>0 denotesthe capacity of p. In this paper, we present the first linear time algorithmfor finding a minimum-cost one-dimensional LCMM (OLCMM) between S and T, whereS and T are points lying on a line, and the cost of matching p in S to q in Tequals the l_2 distance between p,q. Our algorithm improves the previousbest-known quadratic time algorithm.

A faster algorithm for the limited-capacity many-to-many point matching in one dimension