Complexity analysis for maximum flow problems with arc reversals

Rebennack, Steffen; Arulselvan, Ashwin; Elefteriadou, Lily

doi:10.1007/s10878-008-9175-8

Cited by 83 publications

(148 citation statements)

References 14 publications

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“…Algorithm 1. (Rebennack et al, 2010) With natural transformation, we solve the maximum continuous dynamic flow (MCDCF) problem on two terminal network , see (Pyakurel and Dhamala, 2015b). The problem seeks to find a maximum flow that can be sent from the source to the sink within time interval .…”

Section: Methodsmentioning

confidence: 99%

“…Strongly polynomial time algorithms for the problems of maximizing a static flow and a dynamic flow are presented in (Rebennack et al, 2010). But, this problem is -hard in general.…”

Section: Discrete Flows Over Timementioning

confidence: 99%

“…The computational results on the case study has been justified the validness and usefulness of their integrated contraflow model for evacuation planning problem. Rebennack et al (2010) analytically study network flow problems with arc reversal capability. They solve the two-terminal maximum dynamic contraflow (MDCF) problem with discrete time setting.…”

Section: Integrated Approachesmentioning

confidence: 99%

See 2 more Smart Citations

Significance of Transportation Network Models in Emergency Planning of Cities

Dhamala

Pyakurel

2016

CPP

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Transportation network models within the framework of operations research have been established as one of the emerging field of research frontiers in today's very disastrous life and dense traffic system. The discrete as well as continuous flow over time models have been widely considered by social, engineering and applied scientists with wide varieties of real-life problems, like rush hour traffic and traffic management at the time of any disaster. Among the PPRR classification issues, the concentration will be given within the planning approach with transportation networks for urban cities.We present the models and solution strategies of the transportation networks that are dynamic in nature and directly apply in rush hour traffic or human-made or natural disasters in the urban cities. The difficulty levels of the varieties of algorithms, efficiencies of their solution software and the significance of the obtained solutions for the betterment of modern city plan are discussed with wide spectrum of model diversity. Among many others, we illustrate, also supporting with a case study, the impact of recent Nepal Earthquake 2015 and the meaningfulness of effective evacuation planning for saving the property and people in urban city like, Kathmandu, valley.The high performance of the technique of lane reversals in transportation or evacuation networks which has already been adopted a lot in practice, but has been analytically studied only recently are focused in this paper. Adopted this dynamic transportation strategy, the flow in the transportation can be doubled, the time can be saved significantly and many transportation arcs can be utilized for logistic supports or for emergency vehicles whenever necessary. Improved results are presented and the importance of integrated models dependent on time and vehicles is explored. The optimal solution thus obtained with contraflow, logistic supports and facility location at appropriate positions of transportation network proves the significance of these models in emergency planning.

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Section: Methodsmentioning

confidence: 99%

“…Strongly polynomial time algorithms for the problems of maximizing a static flow and a dynamic flow are presented in (Rebennack et al, 2010). But, this problem is -hard in general.…”

Section: Discrete Flows Over Timementioning

confidence: 99%

Section: Integrated Approachesmentioning

confidence: 99%

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Significance of Transportation Network Models in Emergency Planning of Cities

Dhamala

Pyakurel

2016

CPP

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“…If there is only a single source and sink, we can apply the algorithm of Ford and Fulkerson [5] to obtain an orientation and a solution. Furthermore, it was shown that finding the best orientation for a quickest flow problem with multiple sources and sinks is NP-hard [12,15]. Due to the hardness of the problem, heuristic and simulation tools are predominantly used in practice [12,19,20,21].…”

Section: Introductionmentioning

confidence: 99%

Graph Orientation and Flows over Time

Arulselvan

Groß

Skutella

2014

Algorithms and Computation

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Abstract. Flows over time are used to model many real-world logistic and routing problems. The networks underlying such problems -streets, tracks, etc. -are inherently undirected and directions are only imposed on them to reduce the danger of colliding vehicles and similar problems. Thus the question arises, what influence the orientation of the network has on the network flow over time problem that is being solved on the oriented network. In the literature, this is also referred to as the contraflow or lane reversal problem. We introduce and analyze the price of orientation: How much flow is lost in any orientation of the network if the time horizon remains fixed? We prove that there is always an orientation where we can still send 1 3 of the flow and this bound is tight. For the special case of networks with a single source or sink, this fraction is 1 2 which is again tight. We present more results of similar flavor and also show non-approximability results for finding the best orientation for single and multicommodity maximum flows over time.

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“…Transformation of network by reversing the direction of the arc into the ideal direction and reallocating the available capacity for maximizing the flow and minimizing the evacuation time from source to sink is the network contraflow evacuation planning problem. Rebennack et al [21] studied the maximum static contraflow problem for general network, the maximum dynamic contraflow problem and the quickest contraflow problem for two terminal networks and presented the polynomial time algorithms but the quickest transshipment contraflow problem and fixed switching cost contraflow problems are shown NP-hard. Extensive studies with contraflow approach have been made by the authors Dhamala and Pyakurel [4], Pyakurel et al [20], Pyakurel and Dhamala [18], Khadka and Bhandari [15] and Pyakurel and Dhamala [19].…”

mentioning

confidence: 99%

Non-conserving Flow Aspect of Maximum Dynamic Flow Problem

Bhandari

Khadka

2018

J. Inst. Engineering

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Shifting as many people as possible from disastrous area to safer area in a minimum time period in an efficient way is an evacuation planning problem (EPP). Modeling the evacuation scenarios reflecting the real world characteristics and investigation of an efficient solution to them have become a crucial due to rapidly increasing number of natural as well as human created disasters. EPPs modeled on network have been extensively studied and the various efficient solution procedures have been established where the flow function satisfies the flow conservation at each intermediate node. Besides this, the network flow problem in which flow may not be conserved at nodes necessarily could also be useful to model the evacuation planning problem. This paper proposes an efficient solution procedure for maximum flow evacuation planning problem of later kind on a single-source-single-sink dynamic network with integral arc capacities with holding capability of flow (evacuees) in the temporary shelter at intermediate nodes.

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Complexity analysis for maximum flow problems with arc reversals

Cited by 83 publications

References 14 publications

Significance of Transportation Network Models in Emergency Planning of Cities

Significance of Transportation Network Models in Emergency Planning of Cities

Graph Orientation and Flows over Time

Non-conserving Flow Aspect of Maximum Dynamic Flow Problem

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