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Markov chains and polynomial time algorithms

R. Kannan
Proceedings 35th Annual Symposium on Foundations of Computer Science  
This paper outlines the use of rapidly mixing Markov Chains in randomized polynomial time algorithms to solve approximately certain counting problems.  ...  They fall into two classes : combinatorial problems like counting the number of perfect matchings in certain graphs and geometric ones like computing the volumes of convex sets.  ...  Acknowledgement : Many thanks to Alan Frieze and John Mount for reading the manuscript and suggesting many improvements.  ... 
doi:10.1109/sfcs.1994.365726 dblp:conf/focs/Kannan94 fatcat:qoereei67je7fe5jec5gpierdu

Testable Algorithms for Self-Avoiding Walks

Dana Randall, Alistair Sinclair
1994 ACM-SIAM Symposium on Discrete Algorithms  
We present a polynomial time Monte Carlo algorithm for almost uniformly generating and approximately counting self-avoiding walks in rectangular lattices Zd.  ...  These are classical problems that arise, for example, in the study of long polymer chains.  ...  Acknowledgements We thank Neal Madras and Alan Sokal for their valuable comments on an earlier version of this paper.  ... 
dblp:conf/soda/RandallS94 fatcat:ol6wmdqkhfcpxfhgcobwmn3bjm

Phase-type distributions and the structure of finite Markov chains

Robert S. Maier
1993 Journal of Computational and Applied Mathematics  
., Phase-type distributions and the structure of finite Markov chains, Journal of Computational and Applied Mathematics 46 (1993) 449-453.  ...  We show that all discrete phase-type distributions arise as first passage times (i.e., absorption times) in finite-state Markov chains with a certain recursive internal structure.  ...  If (Q, (~1, T,) and (Q, a2, T,) are two Markov chains, whose absorption times r1 and r2 have generating functions Gr(z) and G,(z), then G,(zl(+, )G,(z) arises from a chain with 1 Q, ] + ] Q2 I transient  ... 
doi:10.1016/0377-0427(93)90040-i fatcat:oap2kiqvkfdndhux663moqgo6q

Polynomial time perfect sampling algorithm for two-rowed contingency tables

Shuji Kijima, Tomomi Matsui
2006 Random structures & algorithms (Print)  
The algorithm is based on monotone coupling from the past (monotone CFTP) algorithm and new Markov chain for sampling two-rowed contingency tables uniformly.  ...  This paper proposes a polynomial time perfect (exact) sampling algorithm for 2 × n contingency tables.  ...  In the paper [18] , Propp and Wilson showed that if we have a monotone chain with polynomial time mixing rate, there exists a polynomial time monotone CFTP algorithm.  ... 
doi:10.1002/rsa.20087 fatcat:yfeeofiocrhldimtmyria6ugxu

Polynomial Time Perfect Sampling Algorithm for Two-Rowed Contingency Tables [chapter]

Shuji Kijima, Tomomi Matsui
2004 Mathematics and Computer Science III  
The algorithm is based on monotone coupling from the past (monotone CFTP) algorithm and new Markov chain for sampling two-rowed contingency tables uniformly.  ...  This paper proposes a polynomial time perfect (exact) sampling algorithm for 2 × n contingency tables.  ...  In the paper [18] , Propp and Wilson showed that if we have a monotone chain with polynomial time mixing rate, there exists a polynomial time monotone CFTP algorithm.  ... 
doi:10.1007/978-3-0348-7915-6_18 fatcat:ct5ffolx5jattn3krj55vzgdci

An introduction to computational complexity in Markov Chain Monte Carlo methods

Izhar Asael Alonzo Matamoros
2020 Figshare  
The aim of this work, is to give an introduction to the theoretical background and computational complexity of Markov chain Monte Carlo methods.  ...  In this work we provide a general overview, references and discussion about all this theoretical subjects.  ...  Is hard to visualize that a FPAUS algorithm is equivalent to a Markov chain.  ... 
doi:10.6084/m9.figshare.12124320.v1 fatcat:2uvzikkxvjeutge5mb5lbza7gi

An introduction to computational complexity in Markov Chain Monte Carlo methods [article]

Izhar Asael Alonzo Matamoros
2020 arXiv   pre-print
The aim of this work is to give an introduction to the theoretical background and computational complexity of Markov chain Monte Carlo methods.  ...  In this work, we provide a general overview, references, and discussion about all these theoretical subjects.  ...  Is hard to visualize that a FPAUS algorithm is equivalent to a Markov chain.  ... 
arXiv:2004.07083v1 fatcat:zpahbc65bncdtchrkt5abawrwe

FPRAS Approximation of the Matrix Permanent in Practice [article]

James E. Newman, Moshe Y. Vardi
2020 arXiv   pre-print
We present an implementation and detailed runtime analysis of one such Markov Chain Monte Carlo (MCMC) based Fully Polynomial Randomized Approximation Scheme (FPRAS) for the matrix permanent, which has  ...  It is generally believed to be computationally infeasible for large problem sizes, and significant research has been done on approximation algorithms for the matrix permanent.  ...  is, despite the exponential size of the Markov chain, it converges close to the stationary distribution in polynomial time.  ... 
arXiv:2012.03367v1 fatcat:mfj5qq2s3jff7at6anjbdvblti

The complexity of analyzing infinite-state Markov chains, Markov decision processes, and stochastic games (Invited talk)

Kousha Etessami, Marc Herbstritt
2013 Symposium on Theoretical Aspects of Computer Science  
In particular, I will discuss recent joint work with Alistair Stewart and Mihalis Yannakakis (in papers that appeared at STOC'12 and ICALP'12), in which we have obtained polynomial time algorithms for  ...  In particular, we have studied recursive Markov chains (RMCs), recursive Markov decision processes (RMDPs) and recursive stochastic games (RSGs).  ... 
doi:10.4230/lipics.stacs.2013.1 dblp:conf/stacs/Etessami13 fatcat:jitefxp2brcrxc755si74xdo6q

Interruptible exact sampling in the passive case [article]

Keith Crank, James Allen Fill (Johns Hopkins Univ.)
2002 arXiv   pre-print
Such sampling is possible when enough copies of the chain are available, and we provide an algorithm that terminates with probability one.  ...  We establish, for various scenarios, whether or not interruptible exact stationary sampling is possible when a finite-state Markov chain can only be viewed passively.  ...  In 1995, Lovász and Winkler [10] provided a simpler and more efficient algorithm for obtaining an exact sample from an irreducible N -state Markov chain.  ... 
arXiv:math/0202136v1 fatcat:w66duw7whfawhopn3wpupszali

Hidden Markov model for malicious hosts detection in a computer network

Yakov V. Bubnov, Nick N. Ivanov
2020 Journal of the Belarusian State University. Mathematics and Informatics  
The approach is based on hidden Markov chain model that analyses timeseries and consecutive search of the most probable final state of the model.  ...  Efficiency of the approach is based on assumption that advanced persisted threats are localised in time, therefore malicious hosts in a computer network can be detected by virtue of activity comparison  ...  Fig. 1 . 1 Markov Fig. 2 . 2 Extended Markov chain with two extra equiprobable states Greedy path probability calculation algorithmDijkstra algorithm allows to reach polynomial time complexity of path  ... 
doi:10.33581/2520-6508-2020-3-73-79 fatcat:7igznkbdwnhhpdnagdztvlqph4

The clustered Sparrow algorithm [article]

Cristian Dumitrescu
2018 arXiv   pre-print
In this paper, we study an extension of Schoning's algorithm [Schoning, 1991] for 3SAT, the clustered Sparrow algorithm We also present strong arguments that this algorithm is polynomial.  ...  As a conclusion, the algorithm will hit a solution in at most polynomial time in m (in fact, linear time). Theorem 3. The clustered Sparrow algorithm is polynomial.  ...  We will model the evolution of the algorithm by a Markov chain.  ... 
arXiv:1804.11181v5 fatcat:bgxibregwjhuzfaw6hxzfb23aa

On Counting Perfect Matchings in General Graphs [article]

Daniel Štefankovič, Eric Vigoda, John Wilmes
2017 arXiv   pre-print
, Sinclair, and Vigoda (2004) using a Markov chain Monte Carlo (MCMC) approach.  ...  In fact, it was unresolved whether the same Markov chain defined by JSV is rapidly mixing in general. In this paper, we show that it is not.  ...  The authors are grateful to Santosh Vempala for many illuminating conversations about Markov chains and the structure of factor-critical graphs.  ... 
arXiv:1712.07504v1 fatcat:33nm2t6uhbbvvfcmntraeh2sf4

Understanding the role of noise in stochastic local search: Analysis and experiments

Ole J. Mengshoel
2008 Artificial Intelligence  
To complement existing experimental results, we formulate and analyze several Markov chain models of SLS.  ...  Hitting time analysis using polynomials and convex functions is also discussed.  ...  ) algorithms can be represented by means of discrete-time Markov chains.  ... 
doi:10.1016/j.artint.2007.09.010 fatcat:a3tmgzkr6rgatpzjuwex5667y4

Page 6372 of Mathematical Reviews Vol. , Issue 2004h [page]

2004 Mathematical Reviews  
Tweedie [Markov chains and stochastic stability, Springer, London, 1993; MR 95j:60103]) set C, a geometric (resp. polynomial) rate function r:N — R and the first return time tc for (X,,), to the set C.  ...  Necessary conditions for geometric and polynomial ergodicity of random-walk-type Markov chains. (English summary) Bernoulli 9 (2003), no. 4, 559-578.  ... 
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