On the K best integer network flows
We address the problem of finding the K best integer solutions of a linear integer network flow problem. We design an O(f(n,m,L,U)+KmS(n,m,L)) time and O(K+m) memory space algorithm to determine the K best integer solutions, in a directed network with n nodes, m arcs, maximum absolute value cost L,...
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| Veröffentlicht in: | Computers & operations research 2013-02, Vol.40 (2), p.616-626 |
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| container_title | Computers & operations research |
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| creator | Sedeño-Noda, Antonio Espino-Martín, Juan José |
| description | We address the problem of finding the K best integer solutions of a linear integer network flow problem. We design an O(f(n,m,L,U)+KmS(n,m,L)) time and O(K+m) memory space algorithm to determine the K best integer solutions, in a directed network with n nodes, m arcs, maximum absolute value cost L, and an upper bound U on arc capacities and node supplies. f(n,m,L,U) is the best time needed to solve the minimum cost flow problem in a directed network and S(n,m,L) is the best time to solve the single-source shortest path problem in a network with non-negative lengths. The introduced algorithm efficiently determines a “proper minimal cycle” by taking advantage of the relationship between the best solutions. This way, we improve the theoretical as well as practical memory space bounds of the well-known method due to Hamacher. Our computational experiments confirm this result. |
| doi_str_mv | 10.1016/j.cor.2012.08.014 |
| format | Article |
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We design an O(f(n,m,L,U)+KmS(n,m,L)) time and O(K+m) memory space algorithm to determine the K best integer solutions, in a directed network with n nodes, m arcs, maximum absolute value cost L, and an upper bound U on arc capacities and node supplies. f(n,m,L,U) is the best time needed to solve the minimum cost flow problem in a directed network and S(n,m,L) is the best time to solve the single-source shortest path problem in a network with non-negative lengths. The introduced algorithm efficiently determines a “proper minimal cycle” by taking advantage of the relationship between the best solutions. This way, we improve the theoretical as well as practical memory space bounds of the well-known method due to Hamacher. 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Our computational experiments confirm this result.</description><subject>Algorithms</subject><subject>Applied sciences</subject><subject>Combinatorial optimization</subject><subject>Cost engineering</subject><subject>Cost reduction</subject><subject>Exact sciences and technology</subject><subject>Flows in networks. Combinatorial problems</subject><subject>Integer programming</subject><subject>Integers</subject><subject>K best integer network flow problem</subject><subject>Mathematical models</subject><subject>Minimum cost</subject><subject>Minimum cost flow problem</subject><subject>Network flow problem</subject><subject>Networks</subject><subject>Operational research and scientific management</subject><subject>Operational research. 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Combinatorial problems</topic><topic>Integer programming</topic><topic>Integers</topic><topic>K best integer network flow problem</topic><topic>Mathematical models</topic><topic>Minimum cost</topic><topic>Minimum cost flow problem</topic><topic>Network flow problem</topic><topic>Networks</topic><topic>Operational research and scientific management</topic><topic>Operational research. 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| ispartof | Computers & operations research, 2013-02, Vol.40 (2), p.616-626 |
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| source | ScienceDirect Journals (5 years ago - present) |
| subjects | Algorithms Applied sciences Combinatorial optimization Cost engineering Cost reduction Exact sciences and technology Flows in networks. Combinatorial problems Integer programming Integers K best integer network flow problem Mathematical models Minimum cost Minimum cost flow problem Network flow problem Networks Operational research and scientific management Operational research. Management science Operations research Optimization algorithms Shortest-path problems Studies |
| title | On the K best integer network flows |
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