Dynamic Programming of Optimum Flows in Lossy Communication Nets

Onaga, Kenji

doi:10.1109/tct.1966.1082612

Cited by 37 publications

(31 citation statements)

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“…The following theorem of Onaga [44] says that these are the only two ways to improve the current flow g. It generalizes Theorem 2.2.1.…”

Section: Optimality Conditionsmentioning

confidence: 76%

“…Jewell [33] and Onaga [44]. The generalized maximum flow problem is closely related to the traditional minimum cost flow problem.…”

Section: Combinatorial Methodsmentioning

confidence: 99%

“…Similarly, Onaga's [44] algorithm is analogous to the successive shortest path algorithm developed independently by Busacker and Gowen [7], Iri [30], and Jewell [32]. Truemper's [54] algorithm is an analog of Ford and Fulkerson's [16] primal-dual algorithm.…”

Section: Combinatorial Methodsmentioning

confidence: 99%

“…The problem can also be solved by combinatorial methods, which have led to superior algorithm for many traditional network flow problems. In the 1960's Jewell [33] and Onaga [44] proposed exponential-time augmenting path algorithm for the generalized maximum flow problem. It wasn't until the late 1980's that Goldberg, Plotkin and Tardos [20] designed the first polynomial-time combinatorial algorithms for the generalized maximum flow problem.…”

Section: Literaturementioning

confidence: 99%

“…This is essentially Onaga's [44] algorithm. It generalizes Ford and Fulkerson's [15] augmenting path algorithm for the traditional maximum flow problem.…”

Section: Augmenting Path Algorithmmentioning

confidence: 99%

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Simple Generalized Maximum Flow Algorithms

Tardos

Wayne

1998

Integer Programming and Combinatorial Optimization

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We present several new efficient algorithms for the generalized maximum flow problem. In the traditional maximum flow problem, there is a capacitated network and the goal is to send as much of a single commodity as possible between two distinguished nodes, without exceeding the arc capacity limits. The problem has hundreds of applications including: shipping freight in a transportation network and pumping fluid through a hydraulic network.In traditional networks, there is an implicit assumption that flow is conserved on every arc. Many practical applications violate this conservation assumption.Freight may be damaged or spoil in transit; fluid may leak or evaporate. In generalized networks, each arc has a positive multiplier associated with it, representing the fraction of flow that remains when it is sent along that arc. The generalized maximum flow problem is identical to the traditional maximum flow problem, except that it can also model networks which "leak" flow. Biographical SketchKevin Wayne was born on October 16, 1971 in Philadelphia, Pennsylvania. After failing a placement exam in seventh grade, Kevin was assigned to a remedial math class, where he has found memories of modeling conic sections with clay. By the end of high school, he was taking advanced calculus classes at the University of Pennsylvania, where he realized there was more to math than playing with clay.As an undergraduate at Yale University, Kevin stumbled upon a linear programming course, which introduced him to the area of operations research. In 1993, Yale

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“…The following theorem of Onaga [44] says that these are the only two ways to improve the current flow g. It generalizes Theorem 2.2.1.…”

Section: Optimality Conditionsmentioning

confidence: 76%

“…Jewell [33] and Onaga [44]. The generalized maximum flow problem is closely related to the traditional minimum cost flow problem.…”

Section: Combinatorial Methodsmentioning

confidence: 99%

Section: Combinatorial Methodsmentioning

confidence: 99%

Section: Literaturementioning

confidence: 99%

“…This is essentially Onaga's [44] algorithm. It generalizes Ford and Fulkerson's [15] augmenting path algorithm for the traditional maximum flow problem.…”

Section: Augmenting Path Algorithmmentioning

confidence: 99%

See 3 more Smart Citations