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Abstract flows over time: A first step towards solving dynamic packing problems
Citation key KappmeierMatuschkePeis2012
Author Kappmeier, Jan-Philipp W. and Matuschke, Jannik and Peis, Britta
Title of Book Algorithms and Computation: 23rd International Symposium, ISAAC 2012, Taipei, Taiwan, December 19-21, 2012. Proceedings
Pages 433-443
Year 2012
ISBN 978-3-642-35260-7
Editor Kun-Mao Chao, Tsan-sheng Hsu, and Der-Tsai Lee
Publisher Springer
Series Lecture Notes in Computer Science
Abstract Flows over time generalize classical network ows by introducing a notion of time. Each arc is equipped with a transit time that specifi es how long flow takes to traverse it, while flow rates may vary over time within the given edge capacities. In this paper, we extend this concept of a dynamic optimization problem to the more general setting of abstract flows. In this model, the underlying network is replaced by an abstract system of linearly ordered sets, called "paths" satisfying a simple switching property: Whenever two paths P and Q intersect, there must be another path that is contained in the beginning of P and the end of Q. We show that a maximum abstract flow over time can be obtained by solving a weighted abstract flow problem and constructing a temporally repeated flow from its solution. In the course of the proof, we also show that the relatively modest switching property of abstract networks already captures many essential properties of classical networks.
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Preprints

Preprint 018-2009
Dressler, Daniel and Groß, Martin and Kappmeier, Jan-Philipp and Kelter, Timon and Kulbatzki, Joscha and Plümpe, Daniel and Schlechter, Gordon and Schmidt, Melanie and Skutella, Martin and Temme, Sylvie.
On the Use of Network Flow Techniques for Assigning Evacuees to Exits.


Preprint 001-2012
Kappmeier, Jan-Philipp W. and Matuschke, Jannik and Peis, Britta.
Abstract flows over time: A first step towards solving dynamic packing problems.


Talks

2013
Delegation Visit of the Beijing University of Technology
Technische Universität Berlin, Germany, 31.10.2013
Evacuation Optimization (download)
COGA Doktoranden- & Diplomanden-Seminar
Technische Universität Berlin, Germany, 21.02.2013
How to TikZ?
Lehrstuhl-2-Seminar
Technische Universität Dortmund, Germany, 29.01.2013
Generalizations of Flows over Time and a Fake Application 




2012
International Symposium on Algorithms and Computation
National Taiwan University, 台北市 Taipei, 20.12.2012
Abstract Flows over Time: A First Step towards Solving Dynamic Packing Problems
Berlin-Poznań-Seminar
Freie Universität Berlin, Germany, 10.11.2012
Abstract Flows over Time
International Symposium on Mathematical Programming
Technische Universität Berlin, Germany, 23.08.2012
Flows over Time with Negative Transit Times and Arc Release Dates

International Conference on Evacuation Modeling and Management
Northwestern University, Evanston, USA, 15.08.2012
Evacuation of a 22-Story Building in Simulation and Reality
Cologne Twente Workshop on Graphs and combinatorial Optimization
Universität der Bundeswehr, Munich, Germany, 30.05.2012
Talk on Network Flows over Time with Negative Transit Times and Arc Release Dates.
Tools Seminar
Technische Universität Berlin, Germany, 09.02.2012
How to TikZ?




2010
COGA Doktoranden- & Diplomanden-Seminar
Technische Universität Berlin, Germany, 07.12.2010
How to TikZ? (updated version of 13.12.2010)




2009
International Conference on Evacuation Management 2009
Scheveningen, Netherlands, 24.09.2009
On the Use Network Flow Techniques for Assigning Evacuees to Exits




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