Abstract
In this paper, we consider the quickest flow problem in a network which consists of a directed graph with capacities and transit times on its arcs. We present an O(n logn) time algorithm for the quickest flow problem in a network of grid structure with uniform arc capacity which has a single sink where n is the number of vertices in the network.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Hoppes, B., Tardos, É.: The quickest transshipment problem. Mathematics of Operations Research 25, 36–62 (2000)
Mamada, S., Uno, T., Makino, K., Fujishige, S.: An O(nlog 2 n) algorithm for a sink location problem in dynamic tree networks. Discrete Applied Mathematics (to appear)
Mamada, S., Makino, K., Fujishige, S.: Evacuation problems and dynamic network flows. In: Proc. SICE Annual Conference 2004, pp. 530–535 (2004)
Mamada, S., Uno, T., Makino, K., Fujishige, S.: A tree partitioning problem arising from an evacuation problem in tree dynamic networks. Journal of the Operations Research Society of Japan 48, 196–206 (2005)
Ibaraki, T., Katoh, N.: Resource allocation problems under submodular constraints. In: Resource Allocation Problems: Algorithmic Approaches, pp. 144–176. MIT Press, Cambridge (1988)
Fujishige, S.: Nonlinear optimization with submodular constraints. In: Submodular Functions and Optimization, 2nd edn., pp. 223–250. Elsevier Science Ltd, North-Holland (2005)
Fujishige, S.: Lexicographically optimal base of a polymatroid with respect to a weight vector. Mathematics of Operations Research 5, 186–196 (1980)
Mamada, S., Makino, K., Fujishige, S.: Optimal sink location problem for dynamic flows in a tree network. IEICE Transactions on Fundamentals E85-A, 1020–1025 (2002)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kamiyama, N., Katoh, N., Takizawa, A. (2006). An Efficient Algorithm for Evacuation Problems in Dynamic Network Flows with Uniform Arc Capacity. In: Cheng, SW., Poon, C.K. (eds) Algorithmic Aspects in Information and Management. AAIM 2006. Lecture Notes in Computer Science, vol 4041. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11775096_22
Download citation
DOI: https://doi.org/10.1007/11775096_22
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-35157-3
Online ISBN: 978-3-540-35158-0
eBook Packages: Computer ScienceComputer Science (R0)