A Fast and Efficient algorithm for Many-To-Many Matching of Points with Demands in One Dimension

04/09/2019

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by   Fatemeh Rajabi-Alni, et al.

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Given two point sets S and T, we first study the many-to-many matching with demands problem (MMD problem). In an MMD, each point of one set must be matched to a given number of the points of the other set, and the cost of matching a point to another point is equal to the distance between the two points. We present an O(n^2) time algorithm for computing a one dimensional MMD (OMMD), where the input point sets S and T lie on the line and |S|+|T| = n. Then, we study a generalized version of MMD problem, that is the many-to-many matching with demands and capacities problem (MMDC), that in which each point has a limited capacity in addition to a demand. We give an O(n^2) algorithm for one dimensional MMDC problem