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Solving Evacuation Problems Efficiently--Earliest Arrival Flows with Multiple Sources

Nadine Baumann, Martin Skutella
2006 2006 47th Annual IEEE Symposium on Foundations of Computer Science (FOCS'06)  
While it has previously been observed that an earliest arrival flow still exists for multiple sources, the problem of computing one efficiently has been open for many years.  ...  Earliest arrival flows capture the essence of evacuation planning.  ...  Computing the earliest arrival pattern With Theorem 3.4 we have reduced the problem of computing the earliest arrival pattern to an s-tearliest arrival flow problem and an earliest arrival transshipment  ... 
doi:10.1109/focs.2006.70 dblp:conf/focs/BaumannS06 fatcat:56py3wvnr5awdoeqjqpwkdwt2y

Approximating Earliest Arrival Flows in Arbitrary Networks [chapter]

Martin Groß, Jan-Philipp W. Kappmeier, Daniel R. Schmidt, Melanie Schmidt
2012 Lecture Notes in Computer Science  
If multiple sinks are present, it is known that earliest arrival flows do not exist in general.  ...  We address the open question of approximating earliest arrival flows in arbitrary networks with multiple sinks and present constructive approximations of time and value for them.  ...  In the special case of networks with zero transit times, earliest arrival flows exist in networks with either one source or one sink, but not in networks with multiple sources and sinks [4] .  ... 
doi:10.1007/978-3-642-33090-2_48 fatcat:gqstrglgind5jchwjxqwczvzwu

Earliest Arrival Flows with Multiple Sources

Nadine Baumann, Martin Skutella
2009 Mathematics of Operations Research  
While it has previously been observed that an earliest arrival flow still exists for multiple sources, the problem of computing one efficiently has been open for many years.  ...  Earliest arrival flows capture the essence of evacuation planning.  ...  A preliminary version of this work appeared in Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science [1] .  ... 
doi:10.1287/moor.1090.0382 fatcat:c6pjvvvo4bdvtaskatqe5jux3y

Evacuation planning by earliest arrival contraflow

Tanka Nath Dhamala, Urmila Pyakurel
2016 Journal of Industrial and Management Optimization  
We present efficient algorithms to solve the earliest arrival contraflow problem on multiple sources and on multiple sinks networks separately.  ...  with increased outbound arc capacity.  ...  Notice that the earliest arrival flow in networks with multiple sources and/or sinks associated with supplies/demands, where we have to transship the supplies within given time period are sometimes also  ... 
doi:10.3934/jimo.2016028 fatcat:og2lvbk6hvhq5e44v4kidxrnhu

Earliest Arrival Flows in Networks with Multiple Sinks

Melanie Schmidt, Martin Skutella
2010 Electronic Notes in Discrete Mathematics  
We analyze the special case of flows over time with zero transit times and characterize which networks always allow for earliest arrival flows.  ...  Unfortunately, given a network with multiple sinks, flows over time satisfying this condition do not always exist.  ...  Consequentially, a lot of research has been devoted to single-sink networks and algorithms to compute earliest arrival flows in this special situation, both for single-source-single-sink networks [5,  ... 
doi:10.1016/j.endm.2010.05.077 fatcat:ypbo5op4vzetvfnuy6msdjskwq

Earliest arrival flows in networks with multiple sinks

Melanie Schmidt, Martin Skutella
2014 Discrete Applied Mathematics  
We analyze the special case of flows over time with zero transit times and characterize which networks always allow for earliest arrival flows.  ...  Unfortunately, given a network with multiple sinks, flows over time satisfying this condition do not always exist.  ...  Consequentially, a lot of research has been devoted to single-sink networks and algorithms to compute earliest arrival flows in this special situation, both for single-source-single-sink networks [5,  ... 
doi:10.1016/j.dam.2011.09.023 fatcat:tksdskgqbjebdarn3e5k57ct7i

A survey on network contraflow evacuation planningproblems

Phanindra Prasad Bhandari, Shree Ram Khadka
2015 Journal of Science and Engineering  
One of the efficient ways to model the evacuation situation is a network flow optimization model. This model captures most of the necessities of the evacuation planning.  ...  All the works to till date about earliest arrival contraflow problem are of the single sink network as there exists no earliest arrival flow on the multiple sinks network, Gale (1959).  ...  A dynamic flow with both latest departure and earliest arrival property is called a universally maximum dynamic flow. Gale (1959) answered the question of existence of the earliest arrival flow.  ... 
doi:10.3126/jsce.v3i0.22387 fatcat:trj4t6fhebdcvabnasvtcrnywm

On Solving Quickest Time Problems in Time-Dependent, Dynamic Networks

Elise Miller-Hooks, Sarah Stock Patterson
2004 Journal of Mathematical Modelling and Algorithms  
where the arc travel times, arc and node capacities, and supply at the source vary with time.  ...  In this paper, a pseudopolynomial time algorithm is presented for solving the integral time-dependent quickest flow problem (TDQFP) and its multiple source and sink counterparts: the time-dependent evacuation  ...  Acknowledgments The authors are grateful to Hao Tang and Baiyu Yang for their assistance with the computational experiments.  ... 
doi:10.1023/b:jmma.0000026708.57419.6d fatcat:qascbgdoinc4zchceuopxjlwgy

Efficient Algorithms on Multicommodity Flow over Time Problems with Partial Lane Reversals

Urmila Pyakurel, Shiva Prakash Gupta, Durga Prasad Khanal, Tanka Nath Dhamala, Vladimir V. Mityushev
2020 International Journal of Mathematics and Mathematical Sciences  
The maximum flow over time problem concerns to maximize the sum of commodity flows in a given time horizon. It becomes the earliest arrival flow problem if it maximizes the flow at each time step.  ...  The earliest arrival transshipment problem is the one that satisfies specified supplies and demands. These flow over time problems are computationally hard.  ...  In connection to this problem, Gale [8] proposed a more general problem known as the earliest arrival flow problem. e earliest arrival flow problem having multiple sources and sinks with given supplies  ... 
doi:10.1155/2020/2676378 fatcat:5b5nzdf7zfhthc4igmx7x4mn5a

Earliest arrival flows on series-parallel graphs

Stefan Ruzika, Heike Sperber, Mechthild Steiner
2011 Networks  
We present an exact algorithm for computing an earliest arrival flow in a discrete time setting on series-parallel graphs.  ...  In contrast to previous results for the earliest arrival flow problem this algorithm runs in polynomial time.  ...  In networks with multiple sources and multiple sinks with given supplies and demands, an earliest arrival flow does not necessarily exist (see [2] ).  ... 
doi:10.1002/net.20398 fatcat:ctr4moxz5vc2ro3kyow2nvyipy

On the Transit-Based Evacuation Strategies in an Integrated Network Topology

Iswar Mani Adhikari, Tanka Nath Dhamala
2020 The Nepali Mathematical Sciences Report  
The dynamic network flow models for various evacuation network topology have been found suitable for the solution of such a problem.  ...  Arrival patterns of the evacuees including their transshipments at different pickup locations and their assignments are presented.  ...  It is offered by the earliest arrival flows.  ... 
doi:10.3126/nmsr.v37i1-2.34063 fatcat:ezsqqtmaabavhcbppbmam6tm3q

Earliest arrival dynamic flow model for emergency evacuation in fuzzy conditions

E Gerasimenko, I Rozenberg
2020 IOP Conference Series: Materials Science and Engineering  
The proposed method consists in transporting the maximum number of aggrieved in each time interval based on finding the maximum flow of the earliest arrival in a fuzzy dynamic transportation network.  ...  The process of flow conveying is implemented on the network with time-dependent parameters.  ...  The earliest arrival maximum flow problem (universal maximum flow problem) has multiple sources, which unity is denoted by S and the super-source node ′ that integrates all sources.  ... 
doi:10.1088/1757-899x/734/1/012147 fatcat:cauxedegt5civacigweqjiclhe

Selfish Routing on Dynamic Flows [article]

Christine Antonsen
2015 arXiv   pre-print
Selfish routing on dynamic flows over time is used to model scenarios that vary with time in which individual agents act in their best interest.  ...  We then examine how these adjustments affect the computability, optimality, and existence of selfish routings.  ...  Acknowledgments I am grateful for my advisor Alexa Sharp for her support and wisdom, and to the Oberlin College Computer Science Department for giving me this research opportunity.  ... 
arXiv:1507.03498v1 fatcat:jl74l5pwqffelpomu2buhyuo6y

Quickest Flows Over Time

Lisa Fleischer, Martin Skutella
2007 SIAM journal on computing (Print)  
Key words. network flows, flows over time, dynamic flows, quickest flows, earliest arrival flows, approximation algorithms AMS subject classifications. 90B06, 90B10, 90B20, 90C27, 90C35, 90C59, 68Q25,  ...  Recently the term dynamic has been used in many algorithmic settings to refer to problems with input data that arrives online or changes over time, and the goal of the algorithms described is to modify  ...  An earliest arrival flow also exists for the case of multiple sources and a single sink [34] .  ... 
doi:10.1137/s0097539703427215 fatcat:cwrypwojzbhapefdrk7imgg7n4

Network Flow with Intermediate Storage: Models and Algorithms

Urmila Pyakurel, Stephan Dempe
2020 SN Operations Research Forum  
We also study the earliest arrival property of the maximum dynamic flow in two terminal series-parallel networks and present its efficient solution procedure with intermediate storage.  ...  We also solve an earliest arrival contraflow problem with intermediate storage. Our investigation is focused to solve the evacuation planning problem where the intermediate storage is permitted.  ...  As we have |S| = δ, the earliest arrival flow with intermediate storage can be computed in O(δ×(nm+m log m)) time complexity.  ... 
doi:10.1007/s43069-020-00033-0 fatcat:dfyoh2u5cjaxtffnlfwkzyek5e
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