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Optimizing Cost Flows by Modifying Arc Costs and Capacities
[chapter]

2000
*
Lecture Notes in Computer Science
*

An investment on a single

doi:10.1007/3-540-40064-8_12
fatcat:cw54idozpnar3i7rqgawc6obye
*arc*can be used either to decrease the*arc**flow**cost*, or to increase the*arc**capacity*, or both. ... We provide an approximation algorithm on series-parallel graphs which, for arbitrary δ, ε > 0, produces a solution which exceeds the bounds on the budget*and*the*flow**cost**by*factors 1+δ*and*1+ε, respectively ... Preliminaries*and*Problem Formulation A*flow**cost*problem is defined*by*a directed graph G = (V, R) with*arc**capacities*u*and**arc**costs*c. ...##
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Combinatorial algorithms for inverse network flow problems

2002
*
Networks
*

to identify a cycle whose

doi:10.1002/net.10048
fatcat:bjnzl53asnfdvjdyjtzg4ngoue
*cost*divided*by*the number of*arcs*in it is minimum). ... An inverse*optimization*problems is defined as follows: Let S denote the set of feasible solutions of an*optimization*problem P, let c be a specified*cost*vector,*and*xO be a given feasible solution. ... We also acknowledge the help of Don Wagner who raised some perceptive*and*fundamental questions that led to the pursuit of the research reported in this paper. ...##
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Capacity inverse minimum cost flow problem

2008
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Journal of combinatorial optimization
*

Given a directed graph G = (N, A) with

doi:10.1007/s10878-008-9159-8
fatcat:s5zvml36mbahndgsc2bwzvbg54
*arc**capacities*u ij*and*a minimum*cost**flow*problem defined on G, the*capacity*inverse minimum*cost**flow*problem is to find a new*capacity*vector u for the*arc*set ...*By*reduction from the feedback*arc*set problem we show that the*capacity*inverse minimum*cost**flow*problem is N P-hard in the rectilinear case. ... Our goal is to close the gap between the*capacity*perturbing inverse problems*and*the*cost*perturbing ones*by*analyzing the inverse minimum*cost**flow*problem, in which only the*arc**capacities*are changed ...##
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A faster capacity scaling algorithm for minimum cost submodular flow

2002
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Mathematical programming
*

Our algorithm

doi:10.1007/s101070100253
fatcat:bsp6apx4arcnxfbeknk3lq5yyi
*modifies**and*extends the Edmonds-Karp*capacity*scaling algorithm for minimum*cost**flow*to solve the minimum*cost*submodular*flow*problem. ...*Capacities*are relaxed*by*attaching a complete directed graph with uniform*arc**capacity*δ in each scaling phase. ... on related topics,*and*a referee for prompting us to consider the crossing submodular function case. ...##
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Efficient algorithm for Minimum cost flow problem with partial lane reversals

2019
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The Nepali Mathematical Sciences Report
*

We present

doi:10.3126/nmsr.v36i1-2.29970
fatcat:plaizb6oszbqxp52xkhc43hmui
*modified*minimum*cost**flow*algorithm that computes the maximum dynamic*and*the earliest arrival*flows*in strongly polynomial time*and*also preserves all unused*arc**capacities*. ... We also present strongly polynomial time minimum*cost*partial contraflow algorithm that solves both problems with partial reversals of*arc**capacities*on two terminal series parallel networks. ... In this paper, we*modify*the minimum*cost**flow*algorithm of Ruzika et al. [18]*and*obtain the earliest arrival*flow*on TTSP-network*by*saving all unused*arc**capacities*. ...##
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Flow Improvement in Evacuation Planning with Budget Constrained Switching Costs

2020
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International Journal of Mathematics and Mathematical Sciences
*

Different

doi:10.1155/2020/1605806
fatcat:ws4hc3iakbcodh57d5je46zrxy
*flow*improvement strategies with respect to fixed switching*cost*will be investigated, namely, integral, rational,*and*either to increase the full*capacity*of an*arc*or not at all. ... Here, the contraflow approach reverses the direction of*arcs*with respect to the lane reversal*costs*to increase the*flow*value. ... Acknowledgments e first author thanks the University Grants Commission, Nepal, for the PhD research fellowship. e authors would also like to thank the anonymous referees*and*the editor for their valuable ...##
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A Multi-Agent Min-Cost Flow problem with Controllable Capacities - Complexity of Finding a Maximum-flow Nash Equilibrium

english

2014
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Proceedings of the 3rd International Conference on Operations Research and Enterprise Systems
*

english

It can be seen as a basic multi-agent transportation problem where every agent can control the

doi:10.5220/0004765500270034
dblp:conf/icores/FakhfakhBH14
fatcat:un3nbt32erfmlf2huunncwehoq
*capacities*of a set of elementary routes (modeled as*arcs*inside a network), each agent incurring a*cost*proportional ... A Multi-Agent Minimum-*Cost**Flow*problem is addressed in this paper. ... ACKNOWLEDGEMENTS This work was supported*by*the ANR project no. ANR-13-BS02-0006-01 named Athena. ...##
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Finding minimum-cost flows by double scaling

1992
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Mathematical programming
*

In this paper we combine several of these techniques to yield an algorithm running in O(nm log log U log(nC)) time on networks with n vertices, m

doi:10.1007/bf01585705
fatcat:w6rdm5puc5a7lgwipalvbooq7m
*arcs*, maximum*arc**capacity*U,*and*maximum*arc**cost*magnitude ... In addition, we discuss a*capacity*-bounding approach to the minimum-*cost**flow*problem. 1 k S od d anagem, M.IT., Cwnbridge, MA 02139. ... Introduction The minimwn-*cost*circulation problem calls for finding a circulation of minimum*cost*in a network whose*arcs*have*flow**capacities**and**costs*per unit of*flow*. ...##
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Flow Increment through Network Expansion

2021
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Mathematics
*

In this problem, the

doi:10.3390/math9182308
fatcat:kepu4d5tjbfh7guvvage2y3qlm
*flow*augmentation can be achieved either*by*increasing the*capacities*on the existing*arcs*, or*by*adding new*arcs*to the network. ... In this paper, the problem of finding the minimum network expansion*cost*so that the*modified*network can transport a given amount of*flow*from the source node to the sink node is studied. ... The minimum*cost*expansion of the network G (*by*increasing the*capacities*of the*arcs**and**by*adding new*arcs*) has to be found so that in the resulting network G , w units of*flow*can be transported from ...##
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A capacity scaling algorithm for the constrained maximum flow problem

1995
*
Networks
*

Our algorithms are generalizations of the

doi:10.1002/net.3230250207
fatcat:rei43elxibevris3puiiqk2zsm
*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 ... In this paper, we consider two versions of this problem: (i) when the*cost*of*flow*on each*arc*is a linear function of the amount of*flow*,*and*(ii) when the*cost*of*flow*is a convex function of the amount ... In this paper, we answer this question in the affirmative for*capacity*scaling algorithms*and**modify*Edmonds*and*Karp's [4]*capacity*scaling algorithm for the minimum*cost**flow*problem so that it solves ...##
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Finding minimum-cost circulations by canceling negative cycles

1989
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Journal of the ACM
*

A classical algorithm for finding a minimum-

doi:10.1145/76359.76368
fatcat:ndwjlja7l5amtcf5gmieze6irq
*cost*circulation consists of repeatedly finding a residual cycle of negative*cost**and*canceling it*by*pushing enough*flow*around the cycle to saturate an*arc*... A variant of the algorithm that uses dynamic trees runs in O(nm(log n)min{log(nC), m log n)) time on a network of n vertices, m*arcs*,*and**arc**costs*of maximum absolute value C. ... We also would like to thank Serge Plotkin*and*David Shmoys for many helpful comments on preliminary versions of this paper. ...##
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Finding minimum-cost circulations by canceling negative cycles

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

A classical algorithm for finding a minimum-

doi:10.1145/62212.62250
dblp:conf/stoc/GoldbergT88
fatcat:jl5bt3jtvvfnlhxstirfdqxxku
*cost*circulation consists of repeatedly finding a residual cycle of negative*cost**and*canceling it*by*pushing enough*flow*around the cycle to saturate an*arc*... A variant of the algorithm that uses dynamic trees runs in O(nm(log n)min{log(nC), m log n)) time on a network of n vertices, m*arcs*,*and**arc**costs*of maximum absolute value C. ... We also would like to thank Serge Plotkin*and*David Shmoys for many helpful comments on preliminary versions of this paper. ...##
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Efficient Algorithms for Separated Continuous Linear Programs: The Multicommodity Flow Problem with Holding Costs and Extensions

2005
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Mathematics of Operations Research
*

In a network with linear

doi:10.1287/moor.1050.0166
fatcat:7f35cxji75fwhm6prayqeclktu
*flow**costs**and*linear, per-unit-time holding*costs*, our algorithm finds a drainage of the network that, for given constants > 0*and*> 0, has total*cost*1 + OPT + , where OPT is ... We introduce a natural discretization of polynomial size*and*prove that this discretization produces a solution with low*cost*. ... This research was supported in part*by*NSF Career Award CCR-0049071, NSF Award EIA-0049084, NSF Career Award DMI-0093981,*and*an IBM Faculty Partnership Award. ...##
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Combinatorial Approximation Algorithms for Generalized Flow Problems

2001
*
Journal of Algorithms
*

Generalized network

doi:10.1006/jagm.2000.1130
fatcat:jperhhi5m5dthmt6yxccyochoi
*flow*problems generalize normal network*flow*problems*by*specifying a*flow*multiplier for each*arc*. For every unit of*flow*entering the*arc*, units of*flow*exit. ...*flow*, the multicommodity maximum-*flow*,*and*the multicommodity nonnegative-*cost*minimum-*cost**flow*problems. ... Generalized network*flow*models*modify*this conservation*by*associating a*flow*multiplier with each*arc*. For each unit of*flow*sent from vertex along the*arc*, units of*flow*arrive at . ...##
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Algorithms for the Simple Equal Flow Problem

1999
*
Management science
*

We consider the simple equal

doi:10.1287/mnsc.45.10.1440
fatcat:oxqa4vblozegxf4yoa5mmwrkna
*flow*problem in a directed network with n nodes, m*arcs*,*and*where all*arc**capacities**and*node supplies are integer*and*bounded*by*U. ... In this paper, we study a variant of the minimum*cost**flow*problem where we are given a set R ⊆ A of*arcs**and*require that each*arc*in R must carry the same amount of*flow*. ... This research was partially supported*by*the Office of Naval Research under Contract No. N00014-98-1-0317, as well as a grant from the United Parcel Service. ...
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