Parallel computation for well-endowed rings and space-bounded probabilistic machines
Information and Control
A taxonomy of problems with fast parallel algorithms
Information and Control
Pseudorandom number generation and space complexity
Information and Control
How hard is it to marry at random? (On the approximation of the permanent)
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
A new approach to the maximum flow problem
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
Two processor scheduling is in NC
Proc. of the Aegean workshop on computing on VLSI algorithms and architectures
Constructing a perfect matching is in random NC
STOC '85 Proceedings of the seventeenth annual ACM symposium on Theory of computing
NP is as easy as detecting unique solutions
STOC '85 Proceedings of the seventeenth annual ACM symposium on Theory of computing
A Las Vegas RNC algorithm for maximum matching
Combinatorica
Algebraic methods in the theory of lower bounds for Boolean circuit complexity
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
Matching is as easy as matrix inversion
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
NC Algorithms for Comparability Graphs, Interval Gaphs, and Testing for Unique Perfect Matching
Proceedings of the Fifth Conference on Foundations of Software Technology and Theoretical Computer Science
The complexity of elementary algebra and geometry
STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
The complexity of approximate counting
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
The Matching Problem for Strongly Chordal Graphs is in $NC$
The Matching Problem for Strongly Chordal Graphs is in $NC$
Perfect Matching for Regular Graphs is $AC^0$- Hard for the General Matching Problem
Perfect Matching for Regular Graphs is $AC^0$- Hard for the General Matching Problem
Matching Theory (North-Holland mathematics studies)
Matching Theory (North-Holland mathematics studies)
Parity, circuits, and the polynomial-time hierarchy
SFCS '81 Proceedings of the 22nd Annual Symposium on Foundations of Computer Science
Fast parallel matrix and GCD computations
SFCS '82 Proceedings of the 23rd Annual Symposium on Foundations of Computer Science
SFCS '86 Proceedings of the 27th Annual Symposium on Foundations of Computer Science
Interpolating polynomials from their values
Journal of Symbolic Computation - Special issue on computational algebraic complexity
Interpolation of polynomials given by straight-line programs
Theoretical Computer Science
Special issue computational algebraic complexity editorial
Journal of Symbolic Computation - Special issue on computational algebraic complexity
The polynomially bounded perfect matching problem is in NC2
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
Arithmetic Circuits: A survey of recent results and open questions
Foundations and Trends® in Theoretical Computer Science
Detecting lacunary perfect powers and computing their roots
Journal of Symbolic Computation
A new NC-algorithm for finding a perfect matching in d-regular bipartite graphs when d is small
CIAC'06 Proceedings of the 6th Italian conference on Algorithms and Complexity
On the bit-complexity of sparse polynomial and series multiplication
Journal of Symbolic Computation
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It is shown that the problem of deciding and constructing a perfect matching in bipartite graphs G with the polynomial permanents of their n 脳 n adjacency matrices A (perm(A) = nO(1)) are in the deterministic classes NC2 and NC3, respectively. We further design an NC3 algorithm for the problem of constructing all perfect matchings (enumeration problem) in a graph G with a permanent bounded by O(nk). The basic step was the development of a new symmetric functions method for the decision algorithm and the new parallel technique for the matching enumerator problem. The enumerator algorithm works in O(log3 n) parallel time and O(n3k+5.5 ċ log n) processors. In the case of arbitrary bipartite graphs it yields an 'optimal' (up to the log n- factor) parallel time algorithm for enumerating all the perfect matchings in a graph. It 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 matchings in graphs with permanents up to 2nε.