منابع مشابه
Computing Minimum-Weight Perfect Matchings
We make several observations on the implementation of Edmonds’ blossom algorithm for solving minimum-weight perfectmatching problems and we present computational results for geometric problem instances ranging in size from 1,000 nodes up to 5,000,000 nodes. A key feature in our implementation is the use of multiple search trees with an individual dual-change e for each tree. As a benchmark of t...
متن کاملOn the Intersection Number of Matchings and Minimum Weight Perfect Matchings of Multicolored Point Sets
Let P and Q be disjoint point sets with 2k and 2l elements respectively, and M1 and M2 be their minimum weight perfect matchings (with respect to edge lengths). We prove that the edges of M1 and M2 intersect at most |M1| + |M2| − 1 times. This bound is tight. We also prove that P and Q have perfect matchings (not necessarily of minimum weight) such that their edges intersect at most min{r, s} t...
متن کاملOn the ratio between maximum weight perfect matchings and maximum weight matchings in grids
Given a graph G that admits a perfect matching, we investigate the parameter η(G) (originally motivated by computer graphics applications) which is defined as follows. Among all nonnegative edge weight assignments, η(G) is the minimum ratio between (i) the maximum weight of a perfect matching and (ii) the maximum weight of a general matching. In this paper, we determine the exact value of η for...
متن کاملPerfect Matchings in Edge-Transitive Graphs
We find recursive formulae for the number of perfect matchings in a graph G by splitting G into subgraphs H and Q. We use these formulas to count perfect matching of P hypercube Qn. We also apply our formulas to prove that the number of perfect matching in an edge-transitive graph is , where denotes the number of perfect matchings in G, is the graph constructed from by deleting edges with an en...
متن کاملExact minimum degree thresholds for perfect matchings in uniform hypergraphs
Article history: Received 19 August 2011 Available online xxxx Given positive integers k and where 4 divides k and k/2 k−1, we give a minimum -degree condition that ensures a perfect matching in a k-uniform hypergraph. This condition is best possible and improves on work of Pikhurko who gave an asymptotically exact result. Our approach makes use of the absorbing method, as well as the hypergrap...
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ژورنال
عنوان ژورنال: INFORMS Journal on Computing
سال: 1999
ISSN: 1091-9856,1526-5528
DOI: 10.1287/ijoc.11.2.138