A strongly polynomial minimum cost circulation algorithm
Combinatorica
Solving minimum-cost flow problems by successive approximation
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
Faster scaling algorithms for network problems
SIAM Journal on Computing
Faster algorithms for the shortest path problem
Journal of the ACM (JACM)
Finding minimum-cost circulations by successive approximation
Mathematics of Operations Research
Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
SIAM Journal on Computing
Improved Shortest Paths on the Word RAM
ICALP '00 Proceedings of the 27th International Colloquium on Automata, Languages and Programming
Priority Queues: Small, Monotone and Trans-dichotomous
ESA '96 Proceedings of the Fourth Annual European Symposium on Algorithms
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
A double scaling algorithm for the constrained maximum flow problem
Computers and Operations Research
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The constrained maximum flow problem is a variant of the classical maximum flow problem in which the flow from a source node to a sink node is maximized in a directed capacitated network with arc costs subject to the constraint that the total cost of flow should be within a budget. It is important to study this problem because it has important applications, such as in logistics, telecommunications and computer networks; and because it is related to variants of classical problems such as the constrained shortest path problem, constrained transportation problem, or constrained assignment problem, all of which have important applications as well. In this research, we present an O(n^2mlog(nC)) time cost scaling algorithm and compare its empirical performance against the two existing polynomial combinatorial algorithms for the problem: the capacity scaling and the double scaling algorithms. We show that the cost scaling algorithm is on average 25 times faster than the double scaling algorithm, and 32 times faster than the capacity scaling algorithm.