Universally maximum flow with piecewise‐constant capacities

Fleischer, Lisa

doi:10.1002/net.1030

Cited by 25 publications

(5 citation statements)

References 27 publications

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“…Fleischer and Tardos (1998) establish several polynomial time algorithms by natural transformations of discrete flows to continuous ones. Fleischer, L. (2001a) considers the universally maximum flow with at most piecewise constant arc and node capacities to change over time and improves the previous algorithm by a factor of . A continuous linear program for general continuous networks with cost minimization has been formulated given bounded measurable functions of cost, upper bounds, rates of demand or supply and levels of storage in each node, see (Hamacher and Tjandra, 2002).…”

Section: Continuous Flows Over Timementioning

confidence: 99%

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: Continuous Flows Over Timementioning

confidence: 99%

Significance of Transportation Network Models in Emergency Planning of Cities

Dhamala

Pyakurel

2016

CPP

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“…For this problem, Ogier [15] describes an algorithm that uses nl maximum flow computations in a graph on nl nodes and (m + n)l arcs. Fleischer [6] shows how this can be improved to run in the same asymptotic time as one preflow-push maximum flow computation in a graph with nl nodes and (n + m)l arcs. A preflow-push maximum flow algorithm runs in O(mn log(n 2 /m)) time [11] on a graph with n nodes and m arcs.…”

Section: Related Workmentioning

confidence: 99%

“…This special case has been considered in [2,5,6,12,15,22,14], among others. Flows over time with zero transit times capture some time-related issues: they can be used to model instances when network capacities restrict the quantity of flow that can be sent at any one time.…”

Section: Introductionmentioning

confidence: 99%

Optimal Rounding of Instantaneous Fractional Flows Over Time

Fleischer

Orlin

2000

SIAM J. Discrete Math.

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A transshipment problem with demands that exceed network capacity can be solved by sending flow in several waves. How can this be done in the minimum number, T, of waves, and at minimum cost, if costs are piece-wise linear convex functions of the flow? In this paper, we show that this problem can be solved using min{m,logT, l+og(mu)-g(U )} maximum flow computations and one minimum (convex) cost flow computation. Here m is the number of arcs, F is the maximum supply or demand, and U is the maximum capacity. When there is only one sink, this problem can be solved in the same asymptotic time as one minimum (convex) cost flow computation. This improves upon the recent algorithm in [5] which solves the quickest transshipment problem (the above mentioned problem without costs) on k terminals using k logT maximum flow computations and k minimum cost flow computations. Our solutions start with a stationary fractional flow, as described in [5], and use rounding to transform this into an integral flow. The rounding procedure takes O(n) time.

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“…Baumann and Skutella [21]) and zero transit times, in either one source or one sink (cf. Fleischer [22]) earliest arrival transshipment problems, have polynomial time solutions. Gross et al [23] propose efficient algorithms to calculate the approximate earliest arrival flows on arbitrary networks.…”

Section: Introductionmentioning

confidence: 99%

Efficient Dynamic Flow Algorithms for Evacuation Planning Problems with Partial Lane Reversal

et al. 2019

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Contraflow technique has gained a considerable focus in evacuation planning research over the past several years. In this work, we design efficient algorithms to solve the maximum, lex-maximum, earliest arrival, and quickest dynamic flow problems having constant attributes and their generalizations with partial contraflow reconfiguration in the context of evacuation planning. The partial static contraflow problems, that are foundations to the dynamic flows, are also studied. Moreover, the contraflow model with inflow-dependent transit time on arcs is introduced. A strongly polynomial time algorithm to compute approximate solution of the quickest partial contraflow problem on two terminal networks is presented, which is substantiated by numerical computations considering Kathmandu road network as an evacuation network. Our results show that the quickest time to evacuate a flow of value 100,000 units is reduced by more than 42% using the partial contraflow technique, and the difference is more with the increase in the flow value. Moreover, the technique keeps the record of the portions of the road network not used by the evacuees.

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Universally maximum flow with piecewise‐constant capacities

Cited by 25 publications

References 27 publications

Significance of Transportation Network Models in Emergency Planning of Cities

Significance of Transportation Network Models in Emergency Planning of Cities

Optimal Rounding of Instantaneous Fractional Flows Over Time

Efficient Dynamic Flow Algorithms for Evacuation Planning Problems with Partial Lane Reversal

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