On the randomized complexity of volume and diameter

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

Volumn 1992-October, Issue , 1992, Pages 482-491

  Lovasz, Laszlo ^a,b   Simonovits, Miklos ^c,d  

^a EÖTVÖS LORÁND UNIVERSITY   (Hungary)

^b PRINCETON UNIVERSITY   (United States)

^c ALFRÉD RÉNYI INSTITUTE OF MATHEMATICS   (Hungary)

^d RUTGERS UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

MIXING;

CONVEX BODY; CONVEX POLYTOPES; MIXING RATES; RANDOM WALK; RANDOMISED ALGORITHMS; RANDOMIZED ALGORITHMS; STATIONARY DISTRIBUTION; UNIFORM DISTRIBUTION;

MARKOV PROCESSES;

EID: 84990712766     PISSN: 02725428     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/SFCS.1992.267803     Document Type: Conference Paper

References (21)

1. D. Applegate and R. Kannan (1990): Sampling and integration of near log-concave functions (preprint).
2. I. Barany and Z. Furedi (1986): Computing the volume is dim-cult, Proc. of the 18th Annual ACM Symposium on Theory of Computing, pp. 442-447.
3. G. Brightwell and P. Winkler (1990): Counting linear extensions is #P-complete (Bellcore preprint).
4. A. Dinghas (1957), Uber eine Klasse superadditiver Mengen-funktionale von Brunn-Minkowski-Lustemik-schem Typus, Math. Zeitschr. 68, 111-125.
5. M. Dyer and A. Frieze (1988): On the complexity of computing the volume of a poly tope. SIAM J. Comp. 17, 967-974.
6. M. Dyer and A. Frieze (1991): Computing the volume of convex bodies: a case where randomness provably helps (preprint).
7. M. Dyer, A. Frieze and R. Kannan (1989): A Random Polynomial Time Algorithm for Approximating the Volume of Convex Bodies, Proc. of the 21st Annual ACM Symposium on Theory of Computing, 375-381.
8. G. Elekes (1986): A geometric inequality and the complexity of computing volume, Discrete and Computational Geometry 1, 289-292.
9. M. Grotschel, L. Lovasz and A. Schrijver (1988): Geometric Algorithms and Combinatorial Optimization, Springer-Verlag.
10. M. R. Jerrum, L. G. Valiant and V. V. Vazirani (1986): Random generation of combinatorial structures from a uniform distribution, Theoretical Computer Science 43, 169-188.
11. L. G. Khachiyan (1988): On the complexity of computing the volume of a polytope. Izveitia Akad. Nauk SSSR, Engineering Cybernetics 3, 216-217.
12. L. G. Khachiyan (1989): The problem of computing the volume of polytopes is NP-hard. Uspekhi Mat. Nauk 44, 199-200.
13. H. W. Lenstra, Jr. (1983), Integer programming with a fixed number of variables, Oper. Res. 8, 538-548.
14. L. Lovasz (1992): How to compute the volume? Jber. d. Dt. Math.-Verein., Jubilaumstagung 1990, B. G. Teubner, Stuttgart, 138-151.
15. L. Lovasz and M. Simonovits (1990): Mixing rate of Markov chains, an isoperimetric inequality, and computing the volume. Proc. Slst Annual Symp. on Found, of Computer Science, IEEE Computer Soc, 346-355.
16. L. Lovasz and M. Simonovits (1991): Random walks in a convex body and an improved volume algorithm (preprint, Math. Inst. Hung. Acad. Sci. No. 1/1992).
17. N. Metropolis et al: Equation of state calculation by fast computing machines, J. Chem. Physics 21 (1953) 1087-1092.
18. L. E. Payne and H. F. Weinberger (1960): An optimal Poincare inequality for convex domains, Arch. Rat. mech. Anal. 5, 286-292.
19. A. Prekopa (1971), Logarithmic concave measures with applications to stochastic programming, Acta Sci. Math. Szeged. 32 301-316.
20. A. Prekopa (1973), On logarithmic concave measures and functions, Acta Sci. Math. Szeged. 34, 335-343.
21. A. Sinclair and M. Jerrum (1988): Conductance and the rapid mixing property for Markov chains: the approximation of the permanent resolved, Proc. 20th ACM STOC, pp. 235-244.