Abstract
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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Li, Y., Bei, X., Qiao, Y., Tao, D., Chen, Z. (2022). Heterogeneous Multi-commodity Network Flows over Time. In: Kulikov, A.S., Raskhodnikova, S. (eds) Computer Science – Theory and Applications. CSR 2022. Lecture Notes in Computer Science, vol 13296. Springer, Cham. https://doi.org/10.1007/978-3-031-09574-0_15
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DOI: https://doi.org/10.1007/978-3-031-09574-0_15
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