Max flows in O(nm) time, or better
James B. Orlin
- pp 765-774
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TLDR
It is established that the max flow problem is solvable in O(nm) time for all values of n and m, and the running time is improved to O(n2/ log n).Abstract:
In this paper, we present improved polynomial time algorithms for the max flow problem defined on sparse networks with n nodes and m arcs. We show how to solve the max flow problem in O(nm + m31/16 log2 n) time. In the case that m = O(n1.06), this improves upon the best previous algorithm due to King, Rao, and Tarjan, who solved the max flow problem in O(nm logm/(n log n)n) time. This establishes that the max flow problem is solvable in O(nm) time for all values of n and m. In the case that m = O(n), we improve the running time to O(n2/ log n).read more
Citations
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Network Flows
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Journal ArticleDOI
Advances in Quantum Cryptography
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References
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Book
Network Flows: Theory, Algorithms, and Applications
TL;DR: In-depth, self-contained treatments of shortest path, maximum flow, and minimum cost flow problems, including descriptions of polynomial-time algorithms for these core models are presented.
Book ChapterDOI
Maximal Flow Through a Network
L. R. Ford,D. R. Fulkerson +1 more
TL;DR: In this paper, the problem of finding a maximal flow from one given city to another is formulated as follows: "Consider a rail network connecting two cities by way of a number of intermediate cities, where each link has a number assigned to it representing its capacity".
Journal ArticleDOI
Matrix multiplication via arithmetic progressions
Don Coppersmith,Shmuel Winograd +1 more
TL;DR: In this article, a new method for accelerating matrix multiplication asymptotically is presented, based on the ideas of Volker Strassen, by using a basic trilinear form which is not a matrix product.
Book
Network Flows
TL;DR: The question the authors are trying to ask is: how many units of water can they send from the source to the sink per unit of time?
Journal ArticleDOI
Theoretical Improvements in Algorithmic Efficiency for Network Flow Problems
Jack Edmonds,Richard M. Karp +1 more
TL;DR: New algorithms for the maximum flow problem, the Hitchcock transportation problem, and the general minimum-cost flow problem are presented, and Dinic shows that, in a network with n nodes and p arcs, a maximum flow can be computed in 0 (n2p) primitive operations by an algorithm which augments along shortest augmenting paths.
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