Inverse maximum flow and minimum cut problems

Yang, Chao; Zhang, J.; Ma, Zhongfan

doi:10.1080/02331939708844306

Cited by 73 publications

(33 citation statements)

References 4 publications

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“…This problem is studied by Yang, Zhang, and Ma [32]. Using the maximum flow minimum cut duality, they transform the problem into a minimum cost flow problem on an auxiliary digraph with at most 3 |A| arcs.…”

Section: Maximum Flowmentioning

confidence: 99%

“…Section 3.1.1). The constrained case leads to a minimum cost flow problem in an auxiliary network with at most 2 |A| edges (Yang, Zhang, and Ma [32]). The sign constrained case under weighted l 1 norm can also be reduced to a minimum cost flow problem (Ahuja and Orlin [2]).…”

Section: Minimum Cutmentioning

confidence: 99%

“…The single object sign constrained inverse minimum cut problem under unit weight l 1 norm with respect to a given cutŜ is transformed to a maximum flow problem in (V, A \ δ − (Ŝ)) by Yang, Zhang, and Ma [32] and Ahuja and Orlin [3] using combinatorial arguments, and by Ahuja and Orlin [2] using the linear programming approach (cf. Section 3.1.1).…”

Section: Minimum Cutmentioning

confidence: 99%

See 2 more Smart Citations

Inverse Combinatorial Optimization: A Survey on Problems, Methods, and Results

Heuberger

2004

Journal of Combinatorial Optimization

280

152

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Given a (combinatorial) optimization problem and a feasible solution to it, the corresponding inverse optimization problem is to find a minimal adjustment of the cost function such that the given solution becomes optimum.Several such problems have been studied in the last ten years. After formalizing the notion of an inverse problem and its variants, we present various methods for solving them. Then we discuss the problems considered in the literature and the results that have been obtained. Finally, we formulate some open problems.

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Section: Maximum Flowmentioning

confidence: 99%

Section: Minimum Cutmentioning

confidence: 99%

Section: Minimum Cutmentioning

confidence: 99%

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Inverse Combinatorial Optimization: A Survey on Problems, Methods, and Results

Heuberger

2004

Journal of Combinatorial Optimization

280

152

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“…An inverse combinatorial optimization problem consists of modifying some parameters of a network such as capacities or costs, so that a given feasible solution of the direct optimization problem becomes an optimal solution and the distance between the initial vector and the modified vector of parameters is minimum. The inverse maximum flow problem, which is related to the inverse minimum flow problem, has been studied by Yang et al [16]. Strongly polynomial algorithms to solve the inverse maximum flow were presented.…”

Section: Introductionmentioning

confidence: 99%

“…In [16], only the upper bounds for the flow are changed as little as possible in order to make a given feasible flow become a maximum flow.…”

Section: Introductionmentioning

confidence: 99%

Algorithm of the Inverse Minimum Flow Problem With Time-Windows

El-Sherbeny¹

2017

Jour. Math. Sci. Adv. Appl.

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In this paper, we present the inverse minimum flow problem with timewindows, where lower and upper bounds for the flow must be changed as little as possible so that a given feasible flow becomes a minimum flow that satisfies a time-windows constraint for each vertex in the network. A linear time and space method to decide if the problem has solution is presented. The inverse minimum flow problem with time windows has the inverse combinatorial optimization and an NP-hard problem. We propose in this work a new algorithm for solving the 'inverse minimum flow problem with time-windows' (IMFPTW).NASSER A. EL-SHERBENY 2

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An Introduction to Inverse Combinatorial Problems

Demange¹,

Monnot²

2013

Paradigms of Combinatorial Optimization

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Inverse maximum flow and minimum cut problems

Cited by 73 publications

References 4 publications

Inverse Combinatorial Optimization: A Survey on Problems, Methods, and Results

Inverse Combinatorial Optimization: A Survey on Problems, Methods, and Results

Algorithm of the Inverse Minimum Flow Problem With Time-Windows

An Introduction to Inverse Combinatorial Problems

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