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 most Cap(p) elements in T (resp. S), where the function Cap:S\cup T-> Z>0 denotes the capacity of p. In this paper, we present the first linear time algorithm for finding a minimum-cost one-dimensional LCMM (OLCMM) between S and T, where S and T are points lying on a line, and the cost of matching p in S to q in T equals the l_2 distance between p,q. Our algorithm improves the previous best-known quadratic time algorithm.

翻译：给定两个点集S和T，S与T之间的有限容量多对多点匹配（LCMM）将S（或T）中的每个元素p匹配到T（或S）中至少1个且至多Cap(p)个元素，其中函数Cap:S∪T→Z>0表示p的容量。本文提出了首个线性时间算法，用于求解S与T之间的一维最小成本有限容量多对多点匹配（OLCMM），其中S和T为直线上的点，且S中点p与T中点q的匹配成本等于p与q之间的l₂距离。我们的算法改进了此前已知最优的二次时间算法。