An Efficient Implement at ion of Edmonds’ Maximum -Matching
نویسنده
چکیده
A matching in a graph is a collection of edges, no two of which share a
منابع مشابه
Lecture notes for “Analysis of Algorithms”: Maximum matching in general graphs
We present Edmonds’ blossom shrinking algorithm for finding a maximum cardinality matching in a general graph. En route, we obtain an efficient algorithm for finding a minimum vertex cover in a bipartite graph and show that its size is equal to the size of the maximum matching in the graph. We also show that the size of a maximum matching in a general graph is equal to the size of a minimum odd...
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Edmonds d e veloped an efficient a lgorithm for finding in a given graph C a mat c hing of maximum cardinality. Thi s algorithm "s hrinks" part s of the graph C. Although helpful to the intuitive unde rstanding of the theory, s hrinking is compl icated to im plem e nt on an e l<!'c troni c comput e rThe modificati on presente d in thi s paper avoids s hrinking_ It e mploys ins tead a treelik e ...
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Tutte introduced a V by V skew-symmetric matrix T = (tij), called the Tutte matrix, associated with a simple graph G= (V,E). He associates an indeterminate ze with each e ∈ E, then defines tij = ±ze when ij = e ∈ E, and tij = 0 otherwise. The rank of the Tutte matrix is exactly twice the size of a maximum matching of G. Using linear algebra and ideas from the Gallai–Edmonds decomposition, we de...
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We reduce the problem of finding an augmenting path in a general graph to a reachability problem in a directed bipartite graph. A slight modification of depth-first search leads to an algorithm for finding such paths. Although this setting is equivalent to the traditional terminology of blossoms due to Edmonds, there are some advantages. Mainly, this point of view enables the description of alg...
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Given an undirected network G(V,A,c) and a perfect matching M of G, the inverse maximum perfect matching problem consists of modifying minimally the elements of c so that M becomes a maximum perfect matching with respect to the modified vector. In this article, we consider the inverse problem when the modifications are measured by the weighted bottleneck-type Hamming distance. We propose an alg...
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