New facets of the linear ordering polytope

SIAM Journal on Discrete Mathematics

Volumn 12, Issue 3, 1999, Pages 326-336

  Bolotashvili, G ^a   Kovalev, M ^a   Girlich, E ^b  

^a BELARUSIAN STATE UNIVERSITY   (Belarus)

^b OTTO VON GUERICKE UNIVERSITY   (Germany)

Author keywords

Facets; Linear ordering; Linear ordering polytope; Ranking

Indexed keywords

EID: 0037734885     PISSN: 08954801     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0895480196300145     Document Type: Article

References (14)

1. G G. BOLOTASHVILI, On the facets of the permutation polytope, Commun. Georgian Acad. Sci., 121 (1986), pp. 281-284 (in Russian).
2. G. G. BOLOTASHVILI, A Class of Facets of the Permutation Polytope and a Method for Constructing Facets of the Permutation Polytope, Preprint VINITI N3403-B87, Moscow, 1987 (in Russian).
3. G. G. BOLOTASHVILI AND M. M. KOVALEV, The partial order polytope, in Proceedings of the VIII conference "Problems in theoretical cybernetics," Gorky, 1988 (in Russian).
4. V. J. BOWMAN, Permutation polyhedra, SIAM J. Appl. Math., 22 (1972), pp. 586-589.
5. P. FISHBURN, Binary probabilities induced by rankings, SIAM J. Discrete Math., 3 (1990), pp. 478-488.
6. P. FISHBURN, Induced binary probabilities and the linear ordering polytope: A status report, Math. Social Sci., 23 (1992), pp. 67-80.
7. E. GIRLICH, G. G. BOLOTASHVILI, AND M. M. KOVALEV, The poset polytope, in European Chapter on Combinatorial Optimization VIII, Poznan, 1995.
8. M. GRÖTSCHEL, M. JÜNGER, AND G. REINELT, A cutting plane algorithm for the linear ordering problem, Oper. Res., 32 (1984), pp. 1195-1220.
9. M. GRÖTSCHEL, M. JÜNGER, AND G. REINELT, Facets of the linear ordering polytope, Math. Programming, 33 (1985), pp. 43-60.
10. J. LEUNG AND J. LEE, More facets from fences for linear ordering and acyclic subgraph polytopes, Discrete Appl. Math., 50 (1994), pp. 185-200.
11. A. MCLENNAN, Binary stochastic choice, in Preferences, Uncertainty and Optimality, J. S. Chipman, D. McFadden, and M. K. Richter, eds., Westview Press, Boulder, CO, 1990, pp. 187-202.
12. G. REINELT, The Linear Ordering Problem: Algorithms and Applications, Res. Exp. Math. 8, Heldermann Verlag, Berlin, 1985.
13. G. REINELT, A note on small linear ordering polytope, Discrete Comput. Geom., 10 (1993), pp. 67-78.
14. V. A. YEMELICHEV, M. M. KOVALEV, AND M. K. KRAVTSOV, Polytopes, Graphs, Optimization, Cambridge University Press, Cambridge, UK, 1984.