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

Ingo Demgensky, Hartmut Noltemeier, Hans-Christoph Wirth
2000 Lecture Notes in Computer Science  
An investment on a single 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.  ... 
doi:10.1007/3-540-40064-8_12 fatcat:cw54idozpnar3i7rqgawc6obye

Combinatorial algorithms for inverse network flow problems

Ravindra K. Ahuja, James B. Orlin
2002 Networks  
to identify a cycle whose 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.  ... 
doi:10.1002/net.10048 fatcat:bjnzl53asnfdvjdyjtzg4ngoue

Capacity inverse minimum cost flow problem

Çiğdem Güler, Horst W. Hamacher
2008 Journal of combinatorial optimization  
Given a directed graph G = (N, A) with 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  ... 
doi:10.1007/s10878-008-9159-8 fatcat:s5zvml36mbahndgsc2bwzvbg54

A faster capacity scaling algorithm for minimum cost submodular flow

Lisa Fleischer, Satoru Iwata, S. Thomas McCormick
2002 Mathematical programming  
Our algorithm 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.  ... 
doi:10.1007/s101070100253 fatcat:bsp6apx4arcnxfbeknk3lq5yyi

Efficient algorithm for Minimum cost flow problem with partial lane reversals

Urmila Pyakurel
2019 The Nepali Mathematical Sciences Report  
We present 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.  ... 
doi:10.3126/nmsr.v36i1-2.29970 fatcat:plaizb6oszbqxp52xkhc43hmui

Flow Improvement in Evacuation Planning with Budget Constrained Switching Costs

Ram Chandra Dhungana, Tanka Nath Dhamala
2020 International Journal of Mathematics and Mathematical Sciences  
Different 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  ... 
doi:10.1155/2020/1605806 fatcat:ws4hc3iakbcodh57d5je46zrxy

A Multi-Agent Min-Cost Flow problem with Controllable Capacities - Complexity of Finding a Maximum-flow Nash Equilibrium
english

Nadia Chaabane Fakhfakh, Cyril Briand, Marie-José Huguet
2014 Proceedings of the 3rd International Conference on Operations Research and Enterprise Systems  
It can be seen as a basic multi-agent transportation problem where every agent can control the 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.  ... 
doi:10.5220/0004765500270034 dblp:conf/icores/FakhfakhBH14 fatcat:un3nbt32erfmlf2huunncwehoq

Finding minimum-cost flows by double scaling

Ravindra K. Ahuja, Andrew V. Goldberg, James B. Orlin, Robert E. Tarjan
1992 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 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.  ... 
doi:10.1007/bf01585705 fatcat:w6rdm5puc5a7lgwipalvbooq7m

Flow Increment through Network Expansion

Adrian Marius Deaconu, Luciana Majercsik
2021 Mathematics  
In this problem, the 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  ... 
doi:10.3390/math9182308 fatcat:kepu4d5tjbfh7guvvage2y3qlm

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  ...  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  ... 
doi:10.1002/net.3230250207 fatcat:rei43elxibevris3puiiqk2zsm

Finding minimum-cost circulations by canceling negative cycles

Andrew V. Goldberg, Robert E. Tarjan
1989 Journal of the ACM  
A classical algorithm for finding a minimum-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.  ... 
doi:10.1145/76359.76368 fatcat:ndwjlja7l5amtcf5gmieze6irq

Finding minimum-cost circulations by canceling negative cycles

Andrew Goldberg, Robert Tarjan
1988 Proceedings of the twentieth annual ACM symposium on Theory of computing - STOC '88  
A classical algorithm for finding a minimum-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.  ... 
doi:10.1145/62212.62250 dblp:conf/stoc/GoldbergT88 fatcat:jl5bt3jtvvfnlhxstirfdqxxku

Efficient Algorithms for Separated Continuous Linear Programs: The Multicommodity Flow Problem with Holding Costs and Extensions

Lisa Fleischer, Jay Sethuraman
2005 Mathematics of Operations Research  
In a network with linear 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.  ... 
doi:10.1287/moor.1050.0166 fatcat:7f35cxji75fwhm6prayqeclktu

Combinatorial Approximation Algorithms for Generalized Flow Problems

Jeffrey D Oldham
2001 Journal of Algorithms  
Generalized network 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 .  ... 
doi:10.1006/jagm.2000.1130 fatcat:jperhhi5m5dthmt6yxccyochoi

Algorithms for the Simple Equal Flow Problem

Ravindra K. Ahuja, James B. Orlin, Giovanni M. Sechi, Paola Zuddas
1999 Management science  
We consider the simple equal 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.  ... 
doi:10.1287/mnsc.45.10.1440 fatcat:oxqa4vblozegxf4yoa5mmwrkna
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