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dc.contributor.authorLin, Maokai
dc.contributor.authorJaillet, Patrick
dc.date.accessioned2015-12-19T02:05:29Z
dc.date.available2015-12-19T02:05:29Z
dc.date.issued2015
dc.identifier.urihttp://hdl.handle.net/1721.1/100441
dc.description.abstractWe consider the quickest flow problem in dynamic networks with a single source s and a single sink t: given an amount of flow F, find the minimum time needed to send it from s to t, and the corresponding optimal flow over time. We introduce new mathematical formulations and derive optimality conditions for the quickest flow problem. Based on the optimality conditions, we develop a new cost-scaling algorithm that leverages the parametric nature of the problem. The algorithm solves the quickest flow problem with integer arc costs in O(nm log(n[superscript 2]/m) log(nC)) time, where n, m, and C are the number of nodes, arcs, and the maximum arc cost, respectively. Our algorithm runs in the same time bound as the cost-scaling algorithm by Goldberg and Tarjan [10, 11] for solving the min-cost flow problem. This result shows for the first time that the quickest flow problem can be solved within the same time bound as one of the fastest algorithms for the min-cost flow problem. As a consequence, our algorithm will remain one of the fastest unless the quickest flow problem can be shown to be simpler than the min-cost flow problem.en_US
dc.language.isoen_US
dc.publisherSociety for Industrial and Applied Mathematicsen_US
dc.relation.isversionofhttp://dl.acm.org/citation.cfm?id=2722218en_US
dc.rightsCreative Commons Attribution-Noncommercial-Share Alikeen_US
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/4.0/en_US
dc.sourceMIT web domainen_US
dc.titleOn the Quickest Flow Problem in Dynamic Networks - a Parametric Min-Cost Flow Approachen_US
dc.typeArticleen_US
dc.identifier.citationMaokai Lin and Patrick Jaillet. 2015. On the quickest flow problem in dynamic networks: a parametric min-cost flow approach. In Proceedings of the Twenty-Sixth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA '15). SIAM 1343-1356.en_US
dc.contributor.departmentMassachusetts Institute of Technology. Department of Electrical Engineering and Computer Scienceen_US
dc.contributor.departmentMassachusetts Institute of Technology. Operations Research Centeren_US
dc.contributor.mitauthorLin, Maokaien_US
dc.contributor.mitauthorJaillet, Patricken_US
dc.relation.journalProceedings of the 26th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA '15)en_US
dc.eprint.versionAuthor's final manuscripten_US
dc.type.urihttp://purl.org/eprint/type/ConferencePaperen_US
eprint.statushttp://purl.org/eprint/status/NonPeerRevieweden_US
dspace.orderedauthorsLin, Maokai; Jaillet, Patricken_US
dc.identifier.orcidhttps://orcid.org/0000-0002-8585-6566
mit.licenseOPEN_ACCESS_POLICYen_US


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