A faster polynomial algorithm for the constrained maximum flow problem

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 t...

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Bibliographic Details
Published in:Computers & operations research Vol. 39; no. 11; pp. 2634 - 2641
Main Author: CALISKAN, Cenk
Format: Journal Article
Language:English
Published: Kidlington Elsevier Ltd 01.11.2012
Elsevier
Pergamon Press Inc
Subjects:
Algorithms
Applied sciences
Combinatorial analysis
Comparative studies
Computational complexity
Computer science; control theory; systems
Computer systems and distributed systems. User interface
Constraints
Costs
Exact sciences and technology
Flows in networks. Combinatorial problems
Inventory control, production control. Distribution
Logistics
Maximum flow
Minimum cost network flow
Network flow problem
Network flows
Operational research and scientific management
Operational research. Management science
Operations research
Polynomials
Scaling
Shortest-path problems
Software
Transportation problem
Transportation problem (Operations research)
Scaling
Minimum cost network flow
Network flows
Computational complexity
Maximum flow
Costs
Network flow
Assignment problem
Combinatorial problem
Empirical method
Shortest path
Graph theory
Distributed system
Combinatorial optimization
Source sink relationship
Source flow
Transportation problem
Computer network
Time average
Telecommunication network
Budget
Capacity constraint
Optimal flow
Logistics
ISSN:0305-0548, 1873-765X, 0305-0548
Online Access:Get full text
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Summary: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(n2mlog(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.
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ISSN:0305-0548
1873-765X
0305-0548
DOI:10.1016/j.cor.2012.01.010