Constructing a perfect matching is in random NC
Combinatorica
Matching is as easy as matrix inversion
Combinatorica
Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
On the parallel implementation of Goldberg's maximum flow algorithm
SPAA '92 Proceedings of the fourth annual ACM symposium on Parallel algorithms and architectures
Theoretical Improvements in Algorithmic Efficiency for Network Flow Problems
Journal of the ACM (JACM)
Fast Probabilistic Algorithms for Verification of Polynomial Identities
Journal of the ACM (JACM)
Graph Algorithms
Synthesis of Parallel Algorithms
Synthesis of Parallel Algorithms
Improved processor bounds for algebraic and combinatorial problems in RNC
SFCS '85 Proceedings of the 26th Annual Symposium on Foundations of Computer Science
Faster Algebraic Algorithms for Path and Packing Problems
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part I
Finding paths of length k in O∗(2k) time
Information Processing Letters
Determinant Sums for Undirected Hamiltonicity
FOCS '10 Proceedings of the 2010 IEEE 51st Annual Symposium on Foundations of Computer Science
Shortest cycle through specified elements
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Parallel algorithms for the assignment and minimum-cost flow problems
Operations Research Letters
| Hi-index | 0.00 |
We present a new approach to the minimum-cost integral flow problem for small values of the flow. It reduces the problem to the tests of simple multi-variable polynomials over a finite field of characteristic two for non-identity with zero. In effect, we show that a minimum-cost flow of value k in a network with n vertices, a sink and a source, integral edge capacities and positive integral edge costs polynomially bounded in n can be found by a randomized PRAM, with errors of exponentially small probability in n, running in O(klog(kn)+log2 (kn)) time and using 2k(kn)O(1) processors. Thus, in particular, for the minimum-cost flow of value O(logn), we obtain an RNC2 algorithm.