• A combinatorial aggregation al...

Result: A combinatorial aggregation algorithm for stationary distribution of a large Markov chain

Title:
A combinatorial aggregation algorithm for stationary distribution of a large Markov chain
Authors:
GAMBIN, Anna, POKAROWSKI, Piotr
Source:
FCT 2001 : fundamentals of computational theory (Riga, 22-24 August 2001)Lecture notes in computer science. :384-387
Publisher Information:
Berlin: Springer, 2001.
Publication Year:
2001
Physical Description:
print, 7 ref
Original Material:
INIST-CNRS
Subject Terms:
Computer science, Informatique, Sciences exactes et technologie, Exact sciences and technology, Sciences et techniques communes, Sciences and techniques of general use, Mathematiques, Mathematics, Probabilités et statistiques, Probability and statistics, Théorie des probabilités et processus stochastiques, Probability theory and stochastic processes, Processus de markov, Markov processes, Sciences appliquees, Applied sciences, Recherche operationnelle. Gestion, Operational research. Management science, Recherche opérationnelle et modèles formalisés de gestion, Operational research and scientific management, Flots dans les réseaux. Problèmes combinatoires, Flows in networks. Combinatorial problems, Agrégation, Aggregation, Agregación, Arbre graphe, Tree(graph), Arbol grafo, Chaîne Markov, Markov chain, Cadena Markov, Condition stationnaire, Stationary condition, Condición estacionaria, Méthode combinatoire, Combinatorial method, Método combinatorio, Méthode directe, Direct method, Método directo, Méthode espace état, State space method, Método espacio estado, Méthode itérative, Iterative method, Método iterativo, Théorie graphe, Graph theory, Teoría grafo
Document Type:
Conference Conference Paper
File Description:
text
Language:
English
Author Affiliations:
Institute of Informatics, Warsaw University, Banacha 2, 02-097 Warsaw, Poland
Institute of Applied Mathematics, Warsaw University, Banacha 2, 02-097 Warsaw, Poland
ISSN:
0302-9743
Access URL:
http://pascal-francis.inist.fr/vibad/index.php?action=search&terms=1019326
Rights:
Copyright 2001 INIST-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
Notes:
Mathematics

Operational research. Management
Accession Number:
edscal.1019326
Database:
PASCAL Archive

Further Information

A new aggregation algorithm for computing the stationary distribution of a large Markov chain is proposed. This algorithm is attractive when the state space of Markov chain is large enough so that the direct and iterative methods are inefficient. It is based on grouping the states of a Markov chain in such a way that the probability of changing the state inside the group is of greater order of magnitude than interactions between groups. The correctness of the combinatorial aggregation is justified by the method of forest expansions developed recently in [5,6]. In contrast to existing methods our approach is based on combinatorial and graph-theoretic framework and can be seen as an algorithmization of famous Markov Chain Tree Theorem. The general method is illustrated by an example of computing the stationary distribution. We establish also some preliminary results on the complexity of our algorithm. Numerical experiments on several benchmark examples show the potential applicability of the algorithm in real life problems.