A polynomial combinatorial algorithm for generalized minimum cost flow

Wayne, Kevin

doi:10.1145/301250.301261

Cited by 29 publications

(23 citation statements)

References 30 publications

(22 reference statements)

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“…The existence of such an algorithm has been a well-studied and longstanding open problem (see e.g. [9,3,35,26,28]). A strongly polynomial algorithm for a restricted class was given by Adler and Cosares [1].…”

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confidence: 99%

A strongly polynomial algorithm for generalized flow maximization

Végh

2014

Proceedings of the Forty-Sixth Annual ACM Symposium on Theory of Computing

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A strongly polynomial algorithm is given for the generalized flow maximization problem. It uses a new variant of the scaling technique, called continuous scaling. The main measure of progress is that within a strongly polynomial number of steps, an arc can be identified that must be tight in every dual optimal solution, and thus can be contracted. As a consequence of the result, we also obtain a strongly polynomial algorithm for the linear feasibility problem with at most two nonzero entries per column in the constraint matrix.

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confidence: 99%

A strongly polynomial algorithm for generalized flow maximization

Végh

2014

Proceedings of the Forty-Sixth Annual ACM Symposium on Theory of Computing

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“…As such, the objective is to optimize the throughput of the generalized flow as the product of raw flow and the gain factor on each link,  while the traditional capacity and flow conservation constraints still apply to the raw flow. Widely employed in operation research to model the loss, theft, or interest rate in commodity transportation [10][11][12], we find it a good match to the P2P domain. If we assign each peer a resilience factor as the probabilistic measure of its chance of survival within a given time horizon, this resilience factor could be considered as the gain factor in the generalized flow setting.…”

Section: Introductionmentioning

confidence: 89%

“…Exiting works have been focused on unicast routing [10,11]. In particular, Wayne et al [12] present a Dijkstra-variant shortest path algorithm for minimumcost unicast-based generalized flow problem if all gain factors are below one.…”

Section: Related Workmentioning

confidence: 99%

Maximizing Resilient Throughput in Peer-to-Peer Network

Liu¹,

Fan²,

Cao³

et al. 2011

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A unique challenge in P2P network is that the peer dynamics (departure or failure) cause unavoidable disruption to the downstream peers. While many works have been dedicated to consider fault resilience in peer selection, little understanding is achieved regarding the solvability and solution complexity of this problem from the optimization perspective. To this end, we propose an optimization framework based on the generalized flow theory. Key concepts introduced by this framework include resilience factor, resilience index, and generalized throughput, which collectively model the peer resilience in a probabilistic measure. Under this framework, we divide the domain of optimal peer selection along several dimensions including network topology, overlay organization, and the definition of resilience factor and generalized flow. Within each subproblem, we focus on studying the problem complexity and finding optimal solutions. Simulation study is also performed to evaluate the effectiveness of our model and performance of the proposed algorithms.

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“…Subsequent to my thesis, Wayne [58] developed the first efficient primal algorithm for the problem; it repeatedly sends flow along "minimum ratio" augmenting paths or GAPs. His algorithm also extends to solve the generalized minimum cost flow problem; it is the first polynomial-time algorithm for the problem that is not based on general linear programming techniques.…”

Section: Combinatorial Methodsmentioning

confidence: 99%

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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A polynomial combinatorial algorithm for generalized minimum cost flow

Cited by 29 publications

References 30 publications

A strongly polynomial algorithm for generalized flow maximization

A strongly polynomial algorithm for generalized flow maximization

Maximizing Resilient Throughput in Peer-to-Peer Network

Simple Generalized Maximum Flow Algorithms

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