A simple reduction from maximum weight matching to maximum cardinality matching
نویسندگان
چکیده
منابع مشابه
A simple reduction from maximum weight matching to maximum cardinality matching
Let mcm(m,n) and mwm(m,n,N) be the complexities of computing a maximum cardinality matching and a maximum weight matching, and let mcmbi,mwmbi be their counterparts for bipartite graphs, where m,n, and N are the edge count, vertex count, and maximum integer edge weight. Kao, Lam, Sung, and Ting [1] gave a general reduction showing mwmbi(m,n,N) = O(N ·mcmbi(m,n)) and Huang and Kavitha [2] recent...
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A matching in a graph G is a subset M of the edges of G such that no two share an endpoint. A matching has maximum cardinality if its cardinality is at least as large as that of any other matching. An odd-set cover OSC of a graph G is a labeling of the nodes of G with integers such that every edge of G is either incident to a node labeled 1 or connects two nodes labeled with the same number i ≥...
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Several papers have achieved time O( √ nm) for cardinality matching, starting from first principles. This results in a long derivation. We simplify the task by employing well-known concepts for maximum weight matching. We use Edmonds’ algorithm to derive the structure of shortest augmenting paths. We extend this to a complete algorithm for maximum cardinality matching in time O( √ nm).
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Let G be an edge-weighted hypergraph on n vertices, m edges of size O(1), where the edges have real weights in an interval [1, W ]. We show that if we can approximate a maximum weight matching in G within factor α in time T (n,m,W ) then we can find a matching of weight at least (α − ǫ) times the maximum weight of a matching in G in time (ǫ) max 1≤q≤O(ǫ log n ǫ log ǫ−1 ) maxm1+...mq=m ∑q 1 T (n...
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ژورنال
عنوان ژورنال: Information Processing Letters
سال: 2012
ISSN: 0020-0190
DOI: 10.1016/j.ipl.2012.08.010