A new approach to the maximum-flow problem
Journal of the ACM (JACM)
A data structure for dynamic trees
Journal of Computer and System Sciences
Improved time bounds for the maximum flow problem
SIAM Journal on Computing
Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
Efficient minimum cost matching and transportation using the quadrangle inequality
Journal of Algorithms
Dynamic trees as search trees via Euler tours, applied to the network simplex algorithm
Mathematical Programming: Series A and B
A Network Flow Model for Load Balancing in Circuit-Switched Multicomputers
IEEE Transactions on Parallel and Distributed Systems
An algorithm for computing the restriction scaffold assignment problem in computational biology
Information Processing Letters
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The flow decomposition algorithm transforms an arc flow-based solution to a network flow problem into flows on directed paths and cycles. When the undirected graph induced by arcs with positive flow is a tree, a circle, or an augmented tree (with n nodes), the standard implementation of the algorithm runs in O (n2) time. In this article, we exploit the structure of the network to develop an O (n) flow decomposition algorithm. The run-time relies on the property that for these networks, paths or cycles can be represented implicitly in O (1) space. The algorithm is easy to implement and does not use complicated data structures. Because the size of the input is O (n), our algorithm is the fastest possible for flow decomposition on these special networks. Our algorithm can be used to improve run-times for solving matching and transportation problems on trees and circles. © 2012 Wiley Periodicals, Inc. NETWORKS, 2012 © 2012 Wiley Periodicals, Inc.