A new approach to the maximum-flow problem
Journal of the ACM (JACM)
Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
Improved Algorithms for Bipartite Network Flow
SIAM Journal on Computing
A Polynomial Combinatorial Algorithm for Generalized Minimum Cost Flow
Mathematics of Operations Research
Sequential and parallel algorithms for minimum flows
The Korean Journal of Computational & Applied Mathematics
A highest-label preflow algorithm for the minimum flow problem
ICCOMP'07 Proceedings of the 11th WSEAS International Conference on Computers
About preflow algorithms for the minimum flow problem
WSEAS Transactions on Computer Research
Digraphs: Theory, Algorithms and Applications
Digraphs: Theory, Algorithms and Applications
Network information flow with correlated sources
IEEE Transactions on Information Theory
A maximum flow algorithm using MA ordering
Operations Research Letters
Minimum flows in bipartite networks with unit capacities
ICCOMP'09 Proceedings of the WSEAES 13th international conference on Computers
Improved algorithm for minimum flows in bipartite networks with unit capacities
WSEAS Transactions on Computers
WSEAS Transactions on Computers
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In this paper, first we describe the deficit scaling algorithm for minimum flow in bipartite networks. This algorithm is obtained from the deficit scaling algorithm for minimum flow in regular networks developed by Ciupala in [5] by replacing a pull from a node with sufficiently large deficit with two consecutive pulls. This replacement ensures that only nodes in N1 can have deficits. Consequently, the running time of the deficit scaling algorithm for minimum flow is reduced from O(nm+n2 logC) to O(n1m+n12 logC) when it is applied on bipartite networks. In the last part of this paper, we develop a parallel implementation of the deficit scaling algorithm for minimum flow in bipartite networks on an EREW PRAM. The parallel bipartite deficit scaling algorithm performs a pull from an active node with a sufficiently large deficit and with the smallest distance label from N1 at a time followed by a set of pulls from several nodes in N2 in parallel. It runs in O(n12 log C log p) time on an EREW PRAM with p = ⌈m/n1⌉ processors, which is within a logarithmic factor of the running time of the sequential bipartite deficit scaling algorithm for minimum flow.