Compressed polytopes and statistical disclosure limitation

Tohoku Mathematical Journal

Volumn 58, Issue 3, 2006, Pages 433-445

  Sullivant, Seth ^a  

^a HARVARD UNIVERSITY   (United States)

Author keywords

Algebraic statistics; Compressed polytope; Cut polytope; Disclosure limitation; Integer programming

Indexed keywords

EID: 33751024058     PISSN: 00408735     EISSN: None     Source Type: Journal    
DOI: 10.2748/tmj/1163775139     Document Type: Article

References (14)

1. F. BARAHONA AND A. R. MAHJOUB, On the cut polytope. Math. Programming 36 (1986), 157-173.
2. L. BUZZIGOLI AND A. GIUSTI, An algorithm to calculate the lower and upper bounds of the elements of an array given its marginals. Statistical Data Protection Proceedings, 131-147, Eurostat, Luxembourg, 1999.
3. S.D. CHOWDHURY, G. T. DUNCAN, R. KRISHNAN, S. F. ROEHRIG AND S. MUKHERJEE, Disclosure detection in multivariate categorical databases: auditing confidentiality protection through two new matrix operators. Management Science 45 (1999), 1710-1723.
4. M. M. DEZA AND M. LAURENT, Geometry of cuts and metrics. Algorithms Combin. 15, Springer-Verlag, Berlin, 1997.
5. P. DIACONIS AND B. STURMFELS, Algebraic algorithms for sampling from conditional distributions. Ann. Statist. 26 (1998), 363-397.
6. N. ERIKSSON, S. E. FIENBERG, A. RINALDO AND S. SULLIVANT, Polyhedral conditions for the nonexistence of the MLE for hierarchical log-line models, J. Symbolic Comput. 41 (2006), 222-233.
7. E. GAWRILOW AND M. JOSWIG, Polymake: a framework for analyzing convex polytopes, Polytopescombinatorics and computation (Oberwolfach, 1997), DMV Sem. 29, Birkäuser, Basel, 2000.
8. C. HAASE, Lattice polytopes and unimodular triangulations, Dissertation, TU Berlin, 2000.
9. S. HOŞTEN AND B. STURMFELS, Computing the integer programming gap, To appear in Combinatorica, arXiv:math.OC/0301266, 2003.
10. H. OHSUGI AND T. HIBI, Convex polytopes all of whose reverse lexicographic initial ideals are squarefree, Proc. Amer. Math. Soc. 129 (2001), 2541-2546.
11. P.D. SEYMOUR, Matroids and multicommodity flows, European J. Combin. 2 (1981), 257-290.
12. R. STANLEY, Decompositions of rational convex polytopes, Ann. Discrete Math. 6 (1980), 333-342.
13. B. STURMFELS, Gröbner bases and convex polytopes, Univ. Lecture Ser. 8, Amer. Math. Soc., Providence, R.I., 1995.
14. G. ZIEGLER, Lectures on polytopes, Grad. Texts in Math. 152, Springer-Verlag, New York, 1995.