Algebraic Algorithms for Matching and Matroid Problems
نویسندگان
چکیده
منابع مشابه
Algebraic Algorithms for Matching and Matroid Problems
We present new algebraic approaches for several well-known combinatorial problems, including non-bipartite matching, matroid intersection, and some of their generalizations. Our work yields new randomized algorithms that are the most efficient known. For non-bipartite matching, we obtain a simple, purely algebraic algorithm with running time O(n) where n is the number of vertices and ω is the m...
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Basic path-matchings, introduced by Cunningham and Geelen (FOCS 1996), are a common generalization of matroid intersection and non-bipartite matching. The main results of this paper are a new algebraic characterization of basic path-matching problems and an algorithm for constructing basic path-matchings in Õ(nω) time, where n is the number of vertices and ω is the exponent for matrix multiplic...
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Given a set of nodes and edges between them, what’s the maximum of number of disjoint edges? This problem is known as the graph matching problem, and its study has had an enormous impact on the develpoment of algorithms, combinatorics, optimization theory, and even complexity theory. Mathematicians have been interested in the matching problem since the 19th century, leading to celebrated theore...
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Given an undirected graph G = (V,E) and a directed graph D = (V,A), the master/slave matching problem is to find a matching of maximum cardinality in G such that for each arc (u, v) ∈ A with u being matched, v is also matched. This problem is known to be NP-hard in general, but polynomially solvable in a special case where the maximum size of a connected component of D is at most two. This pape...
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ژورنال
عنوان ژورنال: SIAM Journal on Computing
سال: 2009
ISSN: 0097-5397,1095-7111
DOI: 10.1137/070684008