TY - GEN
T1 - A Faster Algorithm for Quickest Transshipments via an Extended Discrete Newton Method
AU - Schloter, Miriam
AU - Skutella, Martin
AU - Tran, Khai Van
N1 - Publisher Copyright:
Copyright © 2022 by SIAM Unauthorized reproduction of this article is prohibited.
PY - 2022
Y1 - 2022
N2 - The Quickest Transshipment Problem is to route ow as quickly as possible from sources with supplies to sinks with demands in a network with capacities and transit times on the arcs. It is of fundamental importance for numerous applications in areas such as logistics, production, trafic, evacuation, and finance. More than 25 years ago, Hoppe and Tardos presented the first (strongly) polynomial-time algorithm for this problem. Their approach, as well as subsequently derived algorithms with strongly polynomial running time, are hardly practical as they rely on parametric submodular function minimization via Megiddo's method of parametric search. The main contribution of this paper is a considerably faster algorithm for the Quickest Transshipment Problem that instead employs a subtle extension of the Discrete Newton Method. This improves the previously best known running time of ~O(m4k14) to ~O(m2k5 + m3k3 + m3n), where n is the number of nodes, m the number of arcs, and k the number of sources and sinks.
AB - The Quickest Transshipment Problem is to route ow as quickly as possible from sources with supplies to sinks with demands in a network with capacities and transit times on the arcs. It is of fundamental importance for numerous applications in areas such as logistics, production, trafic, evacuation, and finance. More than 25 years ago, Hoppe and Tardos presented the first (strongly) polynomial-time algorithm for this problem. Their approach, as well as subsequently derived algorithms with strongly polynomial running time, are hardly practical as they rely on parametric submodular function minimization via Megiddo's method of parametric search. The main contribution of this paper is a considerably faster algorithm for the Quickest Transshipment Problem that instead employs a subtle extension of the Discrete Newton Method. This improves the previously best known running time of ~O(m4k14) to ~O(m2k5 + m3k3 + m3n), where n is the number of nodes, m the number of arcs, and k the number of sources and sinks.
UR - http://www.scopus.com/inward/record.url?scp=85130718466&partnerID=8YFLogxK
M3 - Conference contribution
AN - SCOPUS:85130718466
T3 - Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms
SP - 90
EP - 102
BT - ACM-SIAM Symposium on Discrete Algorithms, SODA 2022
PB - Association for Computing Machinery
T2 - 33rd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2022
Y2 - 9 January 2022 through 12 January 2022
ER -