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New polynomial-time cycle-canceling algorithms for minimum-cost flows

P. T. Sokkalingam, Ravindra K. Ahuja, James B. Orlin
2000 Networks  
In this paper, we describe a new cycle-canceling algorithm that solves the minimum cost flow problem in polynomial time.  ...  The cycle-canceling algorithm is one of the earliest algorithms to solve the minimum cost flow problem.  ...  It is well known that a minimum cost flow problem in a capacitated network can be transformed into a minimum cost flow problem in an uncapacitated network (see, for example, Ahuja, Magnanti and Orlin  ... 
doi:10.1002/1097-0037(200008)36:1<53::aid-net6>3.0.co;2-y fatcat:tvo54whxhvcljinek37wss4tca

Minimum cost network flows: Problems, algorithms, and software

Angelo Sifaleras
2013 Yugoslav Journal of Operations Research  
We present a wide range of problems concerning minimum cost network flows, and give an overview of the classic linear single-commodity Minimum Cost Network Flow Problem (MCNFP) and some other closely related  ...  We also discuss state-of-the-art algorithmic approaches and recent advances in the solution methods for the MCNFP. Finally, optimization software packages for the MCNFP are presented.  ...  ACKNOWLEDGMENTS This research has been partly funded by the Research Committee of the University of Macedonia, Economic and Social Sciences, Greece, under grant 80749 for the advance of Basic Research.  ... 
doi:10.2298/yjor121120001s fatcat:teynps3rx5cmhhkljjuyt5e6v4

A capacity scaling algorithm for the constrained maximum flow problem

Ravindra K. Ahuja, James B. Orlin
1995 Networks  
Our algorithms are generalizations of the capacity scaling algorithms for the minimum cost flow and convex cost flow problems and illustrate the power of capacity scaling algorithms to solve variants of  ...  the minimum cost flow problem in polynomial time.  ...  Since most of the available polynomial-time algorithms for the minimum cost flow problem are scaling-based algorithms, a natural question arises whether we can modify any scaling algorithm for the minimum  ... 
doi:10.1002/net.3230250207 fatcat:rei43elxibevris3puiiqk2zsm

Network Flow Optimization with Minimum Quantities [chapter]

Hans Georg Seedig
2011 Operations Research Proceedings  
In our work, we define the corresponding problem Minimum Cost Network Flow with Minimum Quantities and prove its computational hardness.  ...  In our results, the update step made the inevitable but well-studied subproblem of the initial computation of a minimum cost network flow problem taking most of the actual total running time.  ...  Acknowledgement: The author thanks Prof. Dr. A. Taraz and Dr. Mirko Eickhoff for helpful discussions. Part of this work was done while the author was at Axxom Software AG, Munich, Germany.  ... 
doi:10.1007/978-3-642-20009-0_47 dblp:conf/or/Seedig10 fatcat:vp3mdsd4nvgfbejgikmfpt2zie

A bit-capacity scaling algorithm for the constrained minimal cost network flow problem

Muhammad Tlas
2021 Network Biology  
A polynomial time algorithm for solving the minimum-cost network flow problem has been proposed in this paper.  ...  A generalization of this proposed algorithm has been also performed in order to solve the minimum-cost flow problem in a directed network subject to non-negative lower bound on the flow vector.  ...  Othman, the DG of the AECS for his valuable support and encouragement throughout this work.  ... 
doaj:4154f288caa644309dcd5cd0bf2baba9 fatcat:2yz4m53oxbhsbeu2yxucb4ptr4

A faster strongly polynomial minimum cost flow algorithm

James Orlin
1988 Proceedings of the twentieth annual ACM symposium on Theory of computing - STOC '88  
We present a new strongly polynomial algorithm for the minimum cost flow problem, based on a refinement of the Edmonds-Karp scaling technique.  ...  Using a standard transformation, this approach yields an O(m log n (m + n log n)) algorithm for the capacitated minimum cost flow problem.  ...  Acknowledgements I wish to thank Eva Tardos, Leslie Hall, Serge Plotkin and Bob Tarjan for valuable comments made about this research.  ... 
doi:10.1145/62212.62249 dblp:conf/stoc/Orlin88 fatcat:tcsygvzjbve4nii7onvgzl4tnm

A Faster Strongly Polynomial Minimum Cost Flow Algorithm

James B. Orlin
1993 Operations Research  
We present a new strongly polynomial algorithm for the minimum cost flow problem, based on a refinement of the Edmonds-Karp scaling technique.  ...  Using a standard transformation, this approach yields an O(m log n (m + n log n)) algorithm for the capacitated minimum cost flow problem.  ...  Acknowledgements I wish to thank Eva Tardos, Leslie Hall, Serge Plotkin and Bob Tarjan for valuable comments made about this research.  ... 
doi:10.1287/opre.41.2.338 fatcat:q5sqfflqtvcipfhks5wvx2dljq

Page 1742 of Mathematical Reviews Vol. , Issue 83d [page]

1983 Mathematical Reviews  
Author’s summary: “A method is proposed for solving the minimum cost circulation problem in a network where the arc capacity and the unit flow cost are linear functions cf a parameter.”  ...  Authors’ summary: “An examination is made of a network formulation of a distribution problem, namely, the problem of flow of minimum cost on a generalized network.  ... 

An annotated bibliography of network interior point methods

Mauricio G. C. Resende, Geraldo Veiga
2003 Networks  
network flow algorithms.  ...  This paper presents an annotated bibliography on interior point methods for solving network flow problems.  ...  DLNET, an implementation of the dual affine scaling algorithm for minimum cost capacitated network flow problems is described and tested.  ... 
doi:10.1002/net.10087 fatcat:zwiupodkbbhkrmhm34cxpol4cu

Algorithms for the Simple Equal Flow Problem

Ravindra K. Ahuja, James B. Orlin, Giovanni M. Sechi, Paola Zuddas
1999 Management science  
The minimum cost flow problem is to determine a least cost shipment of a commodity through a network G = (N, A) in order to satisfy demands at certain nodes from available supplies at other nodes.  ...  The capacity scaling algorithm solves it in O(m(m + n log n) log(nU)) time, which is almost the same time needed to solve the minimum cost flow problem by the capacity scaling algorithm.  ...  N00014-98-1-0317, as well as a grant from the United Parcel Service.  ... 
doi:10.1287/mnsc.45.10.1440 fatcat:oxqa4vblozegxf4yoa5mmwrkna

Page 9758 of Mathematical Reviews Vol. , Issue 2003m [page]

2003 Mathematical Reviews  
Our algorithm modifies and extends the Edmonds-Karp capacity scaling algorithm for minimum cost flow to solve the minimum cost submodular flow problem.  ...  Summary: “We describe an O(n*h min{log U,n*logn}) capacity scaling algorithm for the minimum cost submodular flow problem.  ... 

On the Quickest Flow Problem in Dynamic Networks – A Parametric Min-Cost Flow Approach [chapter]

Maokai Lin, Patrick Jaillet
2014 Proceedings of the Twenty-Sixth Annual ACM-SIAM Symposium on Discrete Algorithms  
We consider the quickest flow problem in dynamic networks with a single source s and a single sink t: given an amount of flow F , find the minimum time needed to send it from s to t, and the corresponding  ...  This result shows for the first time that the quickest flow problem can be solved within the same time bound as one of the fastest algorithms for the min-cost flow problem.  ...  Orlin for the help to simplify the proofs for the optimality conditions.  ... 
doi:10.1137/1.9781611973730.89 dblp:conf/soda/LinJ15 fatcat:fml4jr56tve6npz4pwp5thjw4m

A faster polynomial algorithm for the constrained maximum flow problem

Cenk Çalışkan
2012 Computers & Operations Research  
In this research, we present a new polynomial time algorithm that is based on the cost scaling algorithm for the minimum cost network flow problem.  ...  The constrained maximum flow problem is a variant of the classical maximum flow problem in which the total cost of the flow from the source to sink is constrained by a budget limit.  ...  The cost scaling algorithm for the minimum cost network flow problem obtains a series of -optimal solutions with successively smaller values of .  ... 
doi:10.1016/j.cor.2012.01.010 fatcat:2gx4chhcdvblrpqvnj73zr3fca

Simple Generalized Maximum Flow Algorithms [chapter]

Éva Tardos, Kevin D. Wayne
1998 Lecture Notes in Computer Science  
We present several new efficient algorithms for the generalized maximum flow problem.  ...  The generalized maximum flow problem is identical to the traditional maximum flow problem, except that it can also model networks which "leak" flow.  ...  for the minimum cost flow problem, e.g. see [1] .  ... 
doi:10.1007/3-540-69346-7_24 fatcat:uue5a6wtmbckppk5v6pz4ghk64

Uncertain minimum cost flow problem

Sibo Ding
2013 Soft Computing - A Fusion of Foundations, Methodologies and Applications  
After defining the αminimum cost flow, the properties of the model are analyzed, and then an algorithm for uncertain minimum cost flow problem is developed.  ...  The algorithm can be considered as a general solution to the uncertain minimum cost flow problem. To demonstrate the efficiency of the proposed algorithm, a numerical example is illustrated.  ...  Röck (1980) was the first to propose cost scaling algorithm for solving the minimum cost flow problem. Other scholars used ideas from lagrangian relaxation to design new algorithms.  ... 
doi:10.1007/s00500-013-1194-4 fatcat:3fo6qzm5nzgzlfceeftuiq25ta
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