The general maximum matching algorithm of micali and vazirani

Peterson, Paul A.; Loui, Michael C.

doi:10.1007/bf01762129

Cited by 22 publications

(27 citation statements)

References 12 publications

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“…This can be accomplished as follows. Find a maximum matching in the graph using the algorithm of Micali and Vazirani [27], which runs in O m 1/2 p = O m 1.5 n time. Choosing the kite poset for each of the edges in a maximum matching plus one edge for every unmatched vertex yields an optimal solution to COVER KITE(2) .…”

Section: Poset Covermentioning

confidence: 99%

Mining Posets From Linear Orders

Fernandez

Heath

Ramakrishnan

et al. 2013

Discrete Math. Algorithm. Appl.

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There has been much research on the combinatorial problem of generating the linear extensions of a given poset. This paper focuses on the reverse of that problem, where the input is a set of linear orders, and the goal is to construct a poset or set of posets that generates the input. Such a problem finds applications in computational neuroscience, systems biology, paleontology, and physical plant engineering. In this paper, two algorithms are presented for efficiently finding a single poset, if such a poset exists, whose linear extensions are exactly the same as the input set of linear orders. The variation of the problem where a minimum set of posets that cover the input is also explored. This variation is shown to be polynomially solvable for one class of simple posets (kite(2) posets) but NP-complete for a related class (hammock(2,2,2) posets).General Terms: Algorithms.

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Section: Poset Covermentioning

confidence: 99%

Mining Posets From Linear Orders

Fernandez

Heath

Ramakrishnan

et al. 2013

Discrete Math. Algorithm. Appl.

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“…Our approach to computing k-factors uses the maximum matching algorithm by Micali and Vazirani [8,11]. Given a graph G = (V, E), with |V| = n and |E| = m, their algorithm computes a maximum matching in O(n 1/2 m) time.…”

Section: Preliminariesmentioning

confidence: 99%

“…In general, we use the algorithm by Micali and Vazirani [8,11]. Let G = (V, E) be the input graph, with |V| = n, and G = (V , E ) be the inflated graph obtained from G. Notice that the computation of the maximum matching is the most expensive step of the algorithm.…”

Section: Analysis Of the Algorithmmentioning

confidence: 99%

An algorithm for computing simple k-factors

Meijer

Núòez-Rodríguez

Rappaport

2009

Information Processing Letters

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A k-factor of graph G is defined as a k-regular spanning subgraph of G. For instance, a 2-factor of G is a set of cycles that span G. 2-factors have multiple applications in Graph Theory, Computer Graphics, and Computational Geometry [5,4,6,14]. We define a simple 2-factor as a 2-factor without degenerate cycles. In general, simple k-factors are defined as k-regular spanning subgraphs where no edge is used more than once. We propose a new algorithm for computing simple k-factors for all values of k ≥ 2.

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“…We start by describing blossoms. We use the description of Peterson (1985). A blossom exists if there is a bridge (s. t ) and vertices a such that a is an ancestor of both s and t .…”

Section: Blossomsmentioning

confidence: 99%