Dispersion of mass and the complexity of randomized geometric algorithms

Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS

Volumn , Issue , 2006, Pages 729-738

  Rademacher, Luis ^a   Vempala, Santosh ^b  

^a Dept of Aeronautics and Astronautics

^b MIT

Author keywords

[No Author keywords available]

Indexed keywords

CONVEX GEOMETRY; MATRIX PROBLEMS; QUADRATIC LOWER BOUND; RANDOMNESS;

ALGORITHMS; ASYMPTOTIC ANALYSIS; COMPUTATIONAL COMPLEXITY; PROBLEM SOLVING;

COMPUTATIONAL GEOMETRY;

EID: 35348825389     PISSN: 02725428     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/FOCS.2006.26     Document Type: Conference Paper

References (25)

1. D. Applegate and R. Kannan: Sampling and integration of near log-concave functions. Proc. 23th ACM STOC (1990), 156-163.
2. K. Ball: Normed spaces with a weak-Gordon-Lewis property. Functional analysis (Austin, TX, 1987/1989), 36-47, Lecture Notes in Math., 1470, Springer, Berlin, 1991.
3. I. Bárány and Z. Füredi: Computing the Volume is Difficult. Discrete & Computational Geometry 2, (1987), 319-326.
4. A. Björner, L. Lovász, A. Yao: Linear Decision Trees: Volume Estimates and Topological Bounds. In Proc. of the 24th Annu. ACM Symp. on the Theory of Computing (1992): 170-177.
5. S. G. Bobkov and A. Koldobsky: On the central limit property of convex bodies, Geom. Aspects of Funct. Analysis (Milman-Schechtman eds.), Lecture Notes in Math. 1807 (2003).
6. J. Bourgain: On the distribution of polynomials on high dimensional convex sets, Geom. Aspects of Funct. Analysis (Lindenstrauss-Milman eds.), Lecture Notes in Math. 1469 (1991), 127-137.
7. 2/2 on linear search programs for the knapsack problem. J. Comput. Syst. Sci., 16:413-417, 1978.
8. M. Dyer and A. Frieze: Computing the volume of convex bodies: a case where randomness provably helps. Proc. Symp. Appl. Math. 44, (1991), 123-169.
9. M. Dyer, A. Frieze and R. Kannan: A random polynomialtime algorithm for approximating the volume of convex bodies. J. Assoc. Comput. Mach 38 (1991), 1-17.
10. A. Edelman: Eigenvalues and Condition Numbers of Random Matrices. SIAMJ. Matrix Anal. Appl. 9, 4, (1988), 543-560.
11. G. Elekes: A Geometric Inequality and the Complexity of Computing Volume. Discrete & Computational Geometry 1, (1986), 289-292.
12. O. Goldreich and L. Levin: A hard predicate for all oneway functions. In Proc. of the 21st Annu. ACM Symp. on the Theory of Computing, (1989), 25-32.
13. M. Grötschel, L. Lovász, and A. Schrijver: Geometric Algorithms and Combinatorial Optimization, Springer, 1988.
14. M. Jerrum, L. G. Valiant, and V. V. Vazirani: Random generation of combinatorial structures from a uniform distribution. Theoretical Computer Science 43 (1986), 169-188.
15. 5) volume algorithm for convex bodies. Random Structures and Algorithms 11 (1997), 1-50.
16. L. Lovász: How to compute the volume? Jber. d. Dt. Math-Verein, Jubiläumstagung 1990, B. G. Teubner, Stuttgart, 138-151.
17. L. Lovász and M. Simonovits: The Mixing rate of Markov chains, an isoperime trie inequality, and computing the volume. Proc 31st IEEE Annual Symp. on Fo und. of Comp. Sei. (1990), 346-354.
18. L. Lovász and M. Simonovits: Random walks in a convex body and an improved volume algorithm. Random Structures and Alg. A (1993), 359-412.
19. L. Lovász and S. Vempala: The geometry of logconcave functions and sampling algorithms. To appear in Random Structures and Alg.
20. 4) volume algorithm. J. Comp. Sys. Sci. (2006).
21. V.D. Milman and A. Pajor: Isotropic position and inertia ellipsoids and zonoids of the unit ball of a normed ndimensional space. Geometric Aspects of Functional Analysis (1987-88), 64-104, Lecture Notes in Math., 1376. Springer, Berlin (1989)
22. L. Rademacher and S. Vempala: Dispersion of Mass and the Complexity of Randomized Geometric Algorithms. Full version at http ://www-math.mit.edu/ ~lrademac/.
23. M. Simonovits: How to compute the volume in high dimension? Math. Prog. (B), 97, (2003), 337-374.
24. S. Vempala: Geometric Random Walks: A Survey. Combinatorial and Computational Geometry, MSRI 52 (Ed.s J.E. Goodman , J. Pach and E. Welzl), (2005).
25. S. Vempala: The Random Projection Method. Volume 65, DIMACS series in discrete mathematics and theoretical computer science, AMS (2004).