Theoretical Improvements in Algorithmic Efficiency for Network Flow Problems

@article{Edmonds1972TheoreticalII,
  title={Theoretical Improvements in Algorithmic Efficiency for Network Flow Problems},
  author={Jack Edmonds and Richard M. Karp},
  journal={Journal of the ACM (JACM)},
  year={1972},
  volume={19},
  pages={248 - 264}
}
  • J. Edmonds, R. Karp
  • Published 1 April 1972
  • Mathematics, Computer Science
  • Journal of the ACM (JACM)
This paper presents new algorithms for the maximum flow problem, the Hitchcock transportation problem, and the general minimum-cost flow problem. Upper bounds on the numbers of steps in these algorithms are derived, and are shown to compale favorably with upper bounds on the numbers of steps required by earlier algorithms. First, the paper states the maximum flow problem, gives the Ford-Fulkerson labeling method for its solution, and points out that an improper choice of flow augmenting paths… 
The Minimum Cost Flow Problem and The Network Simplex Solution Method
The Minimum Cost Flow (MCF) Problem is to send flow from a set of supply nodes, through the arcs of a network, to a set of demand nodes, at minimum total cost, and without violating the lower and
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  • M. Queyranne
  • Mathematics, Computer Science
    Math. Oper. Res.
  • 1980
TLDR
It is shown that the sequence of flows constructed by Capacity converges toward a maximum flow, which contrasts with the existence of other less “greedy” augmenting path algorithms which are always finite.
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TLDR
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TLDR
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An alternative method based on the preflow concept of Karzanov, which runs as fast as any other known method on dense graphs, achieving an O(n) time bound on an n-vertex graph and faster on graphs of moderate density.
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Until recently, fast algorithms for the maximum flow problem have typically proceeded by constructing layered networks and establishing blocking flows in these networks. However, in recent years, new
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TLDR
A new polynomial time algorithm for solving the minimum cost network flow problem, based on Edmonds-Karp's capacity scaling and Orlin's excess scaling algorithms, which works directly with the given data and original network, and dynamically adjusts the scaling factor between scaling phases.
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TLDR
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References

SHOWING 1-10 OF 13 REFERENCES
On a Class of Capacitated Transportation Problems
Transportation models ordinary and transhipment having certain types of capacity constraints on the flows between origins and destinations are studied from the point of view of transforming them into
Paths, Trees, and Flowers
A graph G for purposes here is a finite set of elements called vertices and a finite set of elements called edges such that each edge meets exactly two vertices, called the end-points of the edge. An
RECEIVED SEPTEMBER
  • RECEIVED SEPTEMBER
  • 1970
Bottleneck extrema
  • 1968
On the equivalence of the capacity-constrained transshipment problem and the Hitchcock problems
  • RAND Corp. Memorandum RM
  • 1960
Apply Algorithm C repeatedly, starting with the pair (f, ~r), until a compatible pair (g, 8) is obtained. Set f = g and ~-= 0
By iteration of Algorithm C, the pair (2f
Note. References [1, 3, 6, 7] are not cited in the text
  • Note. References [1, 3, 6, 7] are not cited in the text
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