An improved parallel algorithm for maximal matching
Information Processing Letters
Efficient algorithms for finding maximum matching in graphs
ACM Computing Surveys (CSUR)
Constructing a perfect matching is in random NC
Combinatorica
Approximation algorithms for weighted matching
Theoretical Computer Science
A catalog of complexity classes
Handbook of theoretical computer science (vol. A)
Parallel algorithms for shared-memory machines
Handbook of theoretical computer science (vol. A)
The complexity of circuit value and network stability
Journal of Computer and System Sciences
Approximating matchings in parallel
Information Processing Letters
Limits to parallel computation: P-completeness theory
Limits to parallel computation: P-completeness theory
Fast parallel algorithms for graph matching problems
Fast parallel algorithms for graph matching problems
Data structures for weighted matching and nearest common ancestors with linking
SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
Linear time 1/2 -approximation algorithm for maximum weighted matching in general graphs
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
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The problem of computing a matching of maximum weight in a given edge-weighted graph is not known to be P-hard or in RNC. This paper presents four parallel approximation algorithms for this problem. The first is an RNC-approximation scheme, i.e., an RNC algorithm that computes a matching of weight at least 1 - Ɛ times the maximum for any given constant Ɛ 0. The second one is an NC approximation algorithm achieving an approximation ratio of 1/2+Ɛ for any fixed Ɛ 0. The third and fourth algorithms only need to know the total order of weights, so they are useful when the edge weights require a large amount of memories to represent. The third one is an NC approximation algorithm that finds a matching of weight at least 2/3Δ+2 times the maximum, where Δ is the maximum degree of the graph. The fourth one is an RNC algorithm that finds a matching of weight at least 1/2Δ+4 times the maximum on average, and runs in O(logΔ) time, not depending on the size of the graph.