A Fast and Efficient algorithm for Many-To-Many Matching of Points with Demands in One Dimension
| Autor: | Rajabi-Alni, Fatemeh, Minaei-Bidgoli, Behrouz, Bagheri, Alireza |
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| Rok vydání: | 2019 |
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| Druh dokumentu: | Working Paper |
| Popis: | Given two point sets S and T, the minimum-cost many-to-many matching with demands (MMD) problem is the problem of finding a minimum-cost many-to-many matching between S and T such that each point of S (respectively T) is matched to at least a given number of the points of T (respectively S). We propose the first O(n^2) time algorithm for computing a one dimensional MMD (OMMD) of minimum cost between S and T, where |S|+|T|=n. In an OMMD problem, the input point sets S and T lie on the real line and the cost of matching a point to another point equals the distance between the two points. We also study a generalized version of the MMD problem, the many-to-many matching with demands and capacities (MMDC) problem, that in which each point has a limited capacity in addition to a demand. We give the first O(n^2) time algorithm for the minimum-cost one dimensional MMDC (OMMDC) problem. Comment: 15 pages,7 figures. arXiv admin note: substantial text overlap with arXiv:1702.01083 |
| Databáze: | arXiv |
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