The DOI matches its Crossref record; 24 of the 24 references it cites were found in a registry or an index.
Random walks in a convex body and an improved volume algorithm
Abstract
We give a randomized algorithm using O(n7 log 2n) separation calls to approximate the volume of a convex body with a fixed relative error. The bound is O(n6 log 4n) for centrally symmpetric bodies and for polytopes with a polynomial number of facets, and O(n5 log 4n) for centrally symmetric polytopes with a polynomial number of facets. We also give an O(n6 log n) algorithm to sample a point from the uniform distribution over a convex body. Several tools are developed that may be interesting on their own. We extend results of Sinclair–Jerrum [43] and the authors [34] on the mixing rate of Markov chains from finite to arbitrary Markov chains. We also analyze the mixing rate of various random walks on convex bodies, in particular the random walk with steps from the uniform distribution over a unit ball. © 1993 John Wiley & Sons, Inc.
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Cites
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Equation of State Calculations by Fast Computing Machines
Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H., & Teller, E. (1953) · The Journal of Chemical Physics · doi:10.1063/1.1699114 · Cited by 37,192
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A Measure of Asymptotic Efficiency for Tests of a Hypothesis Based on the sum of Observations
Chernoff, H. (1952) · The Annals of Mathematical Statistics · doi:10.1214/aoms/1177729330 · Cited by 3,550
Geometric Algorithms and Combinatorial Optimization
Grötschel, M., Lovász, L., & Schrijver, A. (1988) · Algorithms and Combinatorics · doi:10.1007/978-3-642-97881-4 · Cited by 3,431
Self-citationInteger Programming with a Fixed Number of Variables
Lenstra, H. W. (1983) · Mathematics of Operations Research · doi:10.1287/moor.8.4.538 · Cited by 1,440
Alon, N. (1986) · Combinatorica · doi:10.1007/bf02579166 · Cited by 1,137
Random generation of combinatorial structures from a uniform distribution
Jerrum, M. R., Valiant, L. G., & Vazirani, V. V. (1986) · Theoretical Computer Science · doi:10.1016/0304-3975(86)90174-x · Cited by 985
λ1, Isoperimetric inequalities for graphs, and superconcentrators
Alon, N., & Milman, V. D. (1985) · Journal of Combinatorial Theory, Series B · doi:10.1016/0095-8956(85)90092-9 · Cited by 839
Cited by
Local Graph Partitioning using PageRank Vectors
Andersen, R., Chung, F., & Lang, K. (2006) · 2006 47th Annual IEEE Symposium on Foundations of Computer Science (FOCS'06) · doi:10.1109/focs.2006.44 · Cited by 967
The Brunn-Minkowski inequality
Gardner, R. J. (2002) · Bulletin of the American Mathematical Society · doi:10.1090/s0273-0979-02-00941-2 · Cited by 894
Lectures on finite Markov chains
Saloff-Coste, L. (1997) · Lecture Notes in Mathematics · doi:10.1007/bfb0092621 · Cited by 382
Spielman, D. A., & Teng, S.-H. (2013) · SIAM Journal on Computing · doi:10.1137/080744888 · Cited by 316
Metadata
- Authors
- Lovász, L., & Simonovits, M.
- Venue
- Random Structures & Algorithms
- Publisher
- Wiley
- Published
- 1993-01
- Volume
- 4
- Issue
- 4
- Pages
- 359-412
- ISSN
- 1042-9832 (ISSN-L)
- 1098-2418
- OpenAlex
- W2159000620
- Cited by
- 409
- References
- 24
- FWCI
- 12.95
- Type
- journal article
- Language
- en
- Open access
- closed
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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