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

2000
*
Networks
*

In this paper, we describe

doi:10.1002/1097-0037(200008)36:1<53::aid-net6>3.0.co;2-y
fatcat:tvo54whxhvcljinek37wss4tca
*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 ...##
###
Minimum cost network flows: Problems, algorithms, and software

2013
*
Yugoslav Journal of Operations Research
*

We present

doi:10.2298/yjor121120001s
fatcat:teynps3rx5cmhhkljjuyt5e6v4
*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. ...##
###
A capacity scaling algorithm for the constrained maximum flow problem

1995
*
Networks
*

Our

doi:10.1002/net.3230250207
fatcat:rei43elxibevris3puiiqk2zsm
*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*...##
###
Network Flow Optimization with Minimum Quantities
[chapter]

2011
*
Operations Research Proceedings
*

In our work, we define

doi:10.1007/978-3-642-20009-0_47
dblp:conf/or/Seedig10
fatcat:vp3mdsd4nvgfbejgikmfpt2zie
*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. ...##
###
A bit-capacity scaling algorithm for the constrained minimal cost network flow problem

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. ...

##
###
A faster strongly polynomial minimum cost flow algorithm

1988
*
Proceedings of the twentieth annual ACM symposium on Theory of computing - STOC '88
*

We present

doi:10.1145/62212.62249
dblp:conf/stoc/Orlin88
fatcat:tcsygvzjbve4nii7onvgzl4tnm
*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. ...##
###
A Faster Strongly Polynomial Minimum Cost Flow Algorithm

1993
*
Operations Research
*

We present

doi:10.1287/opre.41.2.338
fatcat:q5sqfflqtvcipfhks5wvx2dljq
*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. ...##
###
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

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. ...

##
###
Algorithms for the Simple Equal Flow Problem

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. ...

##
###
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]

2014
*
Proceedings of the Twenty-Sixth Annual ACM-SIAM Symposium on Discrete Algorithms
*

We consider

doi:10.1137/1.9781611973730.89
dblp:conf/soda/LinJ15
fatcat:fml4jr56tve6npz4pwp5thjw4m
*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. ...##
###
A faster polynomial algorithm for the constrained maximum flow problem

2012
*
Computers & Operations Research
*

In this research, we present

doi:10.1016/j.cor.2012.01.010
fatcat:2gx4chhcdvblrpqvnj73zr3fca
*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 . ...##
###
Simple Generalized Maximum Flow Algorithms
[chapter]

1998
*
Lecture Notes in Computer Science
*

We present several

doi:10.1007/3-540-69346-7_24
fatcat:uue5a6wtmbckppk5v6pz4ghk64
*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] . ...##
###
Uncertain minimum cost flow problem

2013
*
Soft Computing - A Fusion of Foundations, Methodologies and Applications
*

After defining

doi:10.1007/s00500-013-1194-4
fatcat:3fo6qzm5nzgzlfceeftuiq25ta
*the*α*minimum**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*. ...
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