Heterogeneous Multi-commodity Network Flows over Time

Publisher:
Springer International Publishing
Publication Type:
Chapter
Citation:
Computer Science – Theory and Applications, 2022, 13296 LNCS, pp. 238-255
Issue Date:
2022-01-01
Full metadata record
In the 1950’s, Ford and Fulkerson introduced dynamic flows by incorporating the notion of time into the network flow model (Oper. Res., 1958). In this paper, motivated by real-world applications including route planning and evacuations, we extend the framework of multi-commodity dynamic flows to the heterogeneous commodity setting by allowing different transit times for different commodities along the same edge. We first show how to construct the time-expanded networks, a classical technique in dynamic flows, in the heterogeneous setting. Based on this construction, we give a pseudopolynomial-time algorithm for the quickest flow problem when there are two heterogeneous commodities. We then present a fully polynomial-time approximation scheme when the nodes have storage for any number of heterogeneous commodities. The algorithm is based on the condensed time-expanded network technique introduced by Fleischer and Skutella (SIAM J. Comput., 2007).
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