Perfect matching for regular graphs is AC 0 -hard for the general matching problem
Elias Dahlhaus,Marek Karpinski +1 more
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It is proved that the perfect matching for regular graphs (even if restricted to degree 3 and 2-connected 4-regular graphs) is $AC^0$-equivalent with the general perfect matching problem for arbitrary graphs.About:
This article is published in Journal of Computer and System Sciences.The article was published on 1992-02-01 and is currently open access. It has received 13 citations till now. The article focuses on the topics: Chordal graph & Strong perfect graph theorem.read more
Citations
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Proceedings ArticleDOI
The matching problem for bipartite graphs with polynomially bounded permanents is in NC
Dima Grigoriev,Marek Karpinski +1 more
TL;DR: An NC3 algorithm for the problem of constructing all perfect matchings in a graph G with a permanent bounded by O(nk) is designed, which entails also among other things an efficient NC3-algorithm for computing small (polynomially bounded) arithmetic permanents, and a sublinear parallel time algorithm for enumerating all the perfect matching in graphs with permanents up to 2nε.
Journal ArticleDOI
Approximating the permanent of graphs with large factors
Paul Dagum,Michael Luby +1 more
TL;DR: The simple algorithm is described, which is an approximation algorithm for the permanent that is a natural simplification of the algorithm suggested by Broder (1986) and analyzed by Jerrum and Sinclair (1988a, b).
Journal ArticleDOI
On the Parallel Complexity of Hamiltonian Cycle and Matching Problem on Dense Graphs
TL;DR: It is proved that finding an NC algorithm for perfect matching in slightly less dense graphs (minimum degree is at least (12 ? ?)|V|) is as hard as the same problem for all graphs, and interestingly the problem of finding a Hamiltonian cycle becomes NP-complete.
Journal Article
Some perfect matchings and perfect half-integral matchings in NC ∗
TL;DR: It is shown that for any class of bipartite graphs which is closed under edge deletion and where the number of perfect matchings can be counted in NC, there is a deterministic NC algorithm for finding a perfect matching.
Book ChapterDOI
The Complexity of Perfect Matching Problems on Dense Hypergraphs
TL;DR: This seems to be the first polynomial time algorithm for the perfect matching problem on hypergraphs for which the existence problem is nontrivial.
References
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Proceedings ArticleDOI
A simple parallel algorithm for the maximal independent set problem
TL;DR: Powerful and general techniques for converting Monte Carlo algorithms into deterministic algorithms are used to convert the Monte Carlo algorithm for the MIS problem into a simple deterministic algorithm with the same parallel running time.
Journal ArticleDOI
A taxonomy of problems with fast parallel algorithms
TL;DR: An attempt is made to identify important subclasses of NC and give interesting examples in each subclass, and a new problem complete for deterministic polynomial time is given, namely, finding the lexicographically first maximal clique in a graph.
Proceedings ArticleDOI
Matching is as easy as matrix inversion
TL;DR: A new algorithm for finding a maximum matching in a general graph that its only computationally non-trivial step is the inversion of a single integer matrix, the isolating lemma, and other applications to parallel computation and randomized reductions are shown.
Book
Algorithmic Graph Theory
TL;DR: Introduction to graph theory algorithmic techniques shortest paths trees and acyclic diagraphs depth first search connectivity and routing graph colouring covers, domination, independent sets, matchings and factors, parallel algorithms computational complexity.
Journal ArticleDOI
Matching is as easy as matrix inversion
TL;DR: A new algorithm for finding a maximum matching in a general graph with special feature is that its only computationally non-trivial step is the inversion of a single integer matrix, the isolating lemma.