Mathematical programming models for some smallest-world problems
Given a weighted graph G, in the minimum-cost-edge-selection problem (MCES), a minimum weighted set of edges is chosen subject to an upper bound on the diameter of graph G. Similarly, in the minimum-diameter-edge-selection problem (MDES), a set of edges is chosen to minimize the diameter subject to...
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| Veröffentlicht in: | Nonlinear analysis: real world applications Jg. 6; H. 5; S. 955 - 961 |
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01.12.2005
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| Abstract | Given a weighted graph
G, in the minimum-cost-edge-selection problem (MCES), a minimum weighted set of edges is chosen subject to an upper bound on the diameter of graph
G. Similarly, in the minimum-diameter-edge-selection problem (MDES), a set of edges is chosen to minimize the diameter subject to an upper bound on their total weight. These problems are shown to be equivalent and proven to be NP-complete. MCES is then formulated as a 0–1 integer programming problem. The problems MCES and MDES provide models for determining smallest-world networks and for measuring the “small-worldness” of graphs. |
|---|---|
| AbstractList | Given a weighted graph
G, in the minimum-cost-edge-selection problem (MCES), a minimum weighted set of edges is chosen subject to an upper bound on the diameter of graph
G. Similarly, in the minimum-diameter-edge-selection problem (MDES), a set of edges is chosen to minimize the diameter subject to an upper bound on their total weight. These problems are shown to be equivalent and proven to be NP-complete. MCES is then formulated as a 0–1 integer programming problem. The problems MCES and MDES provide models for determining smallest-world networks and for measuring the “small-worldness” of graphs. Given a weighted graph G, in the minimum-cost-edge-selection problem (MCES), a minimum weighted set of edges is chosen subject to an upper bound on the diameter of graph G. Similarly, in the minimum-diameter-edge-selection problem (MDES), a set of edges is chosen to minimize the diameter subject to an upper bound on their total weight. These problems are shown to be equivalent and proven to be NP-complete. MCES is then formulated as a 0-1 integer programming problem. The problems MCES and MDES provide models for determining smallest-world networks and for measuring the 'small-worldness' of graphs. |
| Author | Rosenberger, Jay M. Corley, H.W. |
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| Cites_doi | 10.1016/0167-6377(92)90007-P 10.1007/s00453-001-0113-8 10.1002/jgt.3190110315 10.1038/30918 10.1038/35065725 10.1016/S0378-4371(02)00741-0 10.2307/2786545 10.1103/PhysRevLett.87.198701 10.1016/S0377-0427(03)00471-0 10.1109/MCAS.2003.1228503 10.1126/science.286.5439.509 10.1103/RevModPhys.74.47 10.1137/S003614450342480 10.1103/PhysRevE.66.046139 |
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| Keywords | Minimum diameter graphs Binary programming Small world networks |
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Rev. E doi: 10.1103/PhysRevE.66.046139 |
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G, in the minimum-cost-edge-selection problem (MCES), a minimum weighted set of edges is chosen subject to an upper bound on the... Given a weighted graph G, in the minimum-cost-edge-selection problem (MCES), a minimum weighted set of edges is chosen subject to an upper bound on the... |
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