Constructing a perfect matching is in random NC
Combinatorica
A Las Vegas RNC algorithm for maximum matching
Combinatorica
Matrix multiplication via arithmetic progressions
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
Maximum matchings in general graphs through randomization
Journal of Algorithms
Processor efficient parallel solution of linear systems over an abstract field
SPAA '91 Proceedings of the third annual ACM symposium on Parallel algorithms and architectures
Faster scaling algorithms for general graph matching problems
Journal of the ACM (JACM)
Nearly Optimal Algorithms For Canonical Matrix Forms
SIAM Journal on Computing
Flow in Planar Graphs with Multiple Sources and Sinks
SIAM Journal on Computing
Fast Probabilistic Algorithms for Verification of Polynomial Identities
Journal of the ACM (JACM)
Matching is as easy as matrix inversion
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
A New Approach to Maximum Matching in General Graphs
ICALP '90 Proceedings of the 17th International Colloquium on Automata, Languages and Programming
Probabilistic algorithms for sparse polynomials
EUROSAM '79 Proceedings of the International Symposiumon on Symbolic and Algebraic Computation
High-order lifting and integrality certification
Journal of Symbolic Computation - Special issue: International symposium on symbolic and algebraic computation (ISSAC 2002)
Maximum Matchings via Gaussian Elimination
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
An algebraic algorithm for weighted linear matroid intersection
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
MFCS '08 Proceedings of the 33rd international symposium on Mathematical Foundations of Computer Science
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In this paper we consider the problem of finding perfect matchings in parallel. We present a RNC algorithm with optimal work in respect to sequential algorithms, i.e., it uses O(nω) processors.Our algorithm is based on an RNC algorithm for computing determinant of a degree one polynomial matrix, which is of independent interest.