Extended Formulations for Polygons

Discrete and Computational Geometry

Volumn 48, Issue 3, 2012, Pages 658-668

  Fiorini, Samuel ^a   Rothvoß, Thomas ^b   Tiwary, Hans Raj ^a  

^a UNIVERSITÉ LIBRE DE BRUXELLES   (Belgium)

^b MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

Extended formulations; Lower bound; Polygon; Polytope

Indexed keywords

EID: 84865652595     PISSN: 01795376     EISSN: 14320444     Source Type: Journal    
DOI: 10.1007/s00454-012-9421-9     Document Type: Article

References (17)

1. Ajtai, M., Komlós, J., Szemerédi, E.: An O(nlogn) sorting network. In: Proceedings of the Fifteenth Annual ACM Symposium on Theory of Computing, STOC'83, pp. 1-9. ACM, New York (1983).
2. Ben-Tal, A., Nemirovski, A.: On polyhedral approximations of the second-order cone. Math. Oper. Res. 26(2), 193-205 (2001).
3. Cohen, J. E., Rothblum, U. G.: Nonnegative ranks, decompositions, and factorizations of nonnegative matrices. Linear Algebra Appl. 190, 149-168 (1993).
4. Conforti, M., Cornuéjols, G., Zambelli, G.: Extended formulations in combinatorial optimization. 4OR 8(1), 1-48 (2010).
5. Conforti, M., Faenza, Y., Fiorini, S., Grappe, R., Tiwary, H. R.: Extended formulations, non-negative factorizations and randomized communication protocols. http://arxiv. org/abs/1105. 4127 (2011).
6. Fiorini, S., Kaibel, V., Pashkovich, K., Theis, D. O.: Combinatorial bounds on nonnegative rank and extended formulations. Working paper (2011).
7. Goemans, M.: Smallest compact formulation for the permutahedron. http://math. mit. edu/~goemans/PAPERS/permutahedron. pdf (2009).
8. Hindry, M., Silverman, J. H.: Diophantine Geometry: An Introduction, 1st edn. Springer, Berlin (2000).
9. Hungerford, T. W.: Algebra. Graduate Texts in Mathematics. Springer, New York (1974).
10. Kaibel, V.: Extended formulations in combinatorial optimization. Optima 85, 2-7 (2011).
11. Kaibel, V., Pashkovich, K.: Constructing extended formulations from reflection relations. In: Proceedings of the 15th Conference on Integer Programming and Combinatorial Optimization (2011, to appear).
12. Lang, S.: Algebra, Graduate Texts in Mathematics. Springer, Berlin (2002).
13. Martin, R. K.: Using separation algorithms to generate mixed integer model reformulations. Oper. Res. Lett. 10(3), 119-128 (1991).
14. Rothvoß, T.: Some 0/1 polytopes need exponential size extended formulations. http://arxiv. org/abs/1105. 0036 (2011).
15. Stewart, I.: Galois Theory, 3rd edn. Chapman & Hall/CRC Mathematics. Chapman & Hall/CRC, Boca Raton (2004).
16. Vanderbeck, F., Wolsey, L. A.: Reformulation and decomposition of integer programs. In: Jünger, M., et al. (eds.) 50 Years of Integer Programming 1958-2008, pp. 431-502. Springer, Berlin (2010).
17. Yannakakis, M.: Expressing combinatorial optimization problems by linear programs. J. Comput. Syst. Sci. 43(3), 441-466 (1991).