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Maximal Closure of a Graph and Applications to Combinatorial Problems
Abstract
This paper generalizes the selection problem discussed by J. M. Rhys [Rhys, J. M. W. 1970. Shared fixed cost and network flows. Management Sci. 17 (3, November).], J. D. Murchland [Murchland, J. D. 1968. Rhys's combinatorial station selection problem. London Graduate School of Business Studies, Transport Network Theory Unit, Report LBS-TNT-68, June 10.], M. L. Balinski [Balinski, M. L. 1970. On a selection problem. Management Sci. 17 (3, November).] and P. Hansen [Hansen, P. 1974. Quelques approches de la programmation non lineaire en variables 0-1. Conference on Mathematical Programming, Bruxelles, May.]. Given a directed graph G, a closure of G is defined as a subset of nodes such that if a node belongs to the closure all its successors also belong to the set. If a real number is associated to each node of G a maximal closure is defined as a closure of maximal value.
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Cited by
Optimal Surface Segmentation in Volumetric Images-A Graph-Theoretic Approach
Li, K., Wu, X., Chen, D. Z., & Sonka, M. (2006) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2006.19 · Cited by 664
The unconstrained binary quadratic programming problem: a survey
Kochenberger, G., Hao, J.-K., Glover, F., Lewis, M., Lü, Z., Wang, H., & Wang, Y. (2014) · Journal of Combinatorial Optimization · doi:10.1007/s10878-014-9734-0 · Cited by 473
A Fast Parametric Maximum Flow Algorithm and Applications
Gallo, G., Grigoriadis, M. D., & Tarjan, R. E. (1989) · SIAM Journal on Computing · doi:10.1137/0218003 · Cited by 427
Metadata
- Authors
- Picard, J.-C.
- Venue
- Management Science
- Published
- 1976-07
- Volume
- 22
- Issue
- 11
- Pages
- 1268-1272
- ISSN
- 0025-1909 (ISSN-L)
- 1526-5501
- OpenAlex
- W2128208761
- Cited by
- 234
- References
- 0
- FWCI
- 1.07
- Type
- journal article
- Language
- en
- Open access
- closed
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- Picard, J.-C. (1976). Maximal Closure of a Graph and Applications to Combinatorial Problems. Management Science. https://doi.org/10.1287/mnsc.22.11.1268
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