Optimal state-space lumping in Markov chains

Salem Derisavi; H. Hermanns; William H. Sanders

doi:10.1016/S0020-0190(03)00343-0

Optimal state-space lumping in Markov chains

Salem Derisavi
, H. Hermanns
, William H. Sanders

Research output: Contribution to journal › Article › Academic

175 Citations (Scopus)

18 Downloads (Pure)

Abstract

We prove that the optimal lumping quotient of a finite Markov chain can be constructed in O(mlgn) time, where n is the number of states and m is the number of transitions. Our proof relies on the use of splay trees (designed by Sleator and Tarjan [J. ACM 32 (3) (1985) 652–686]) to sort transition weights.

Original language	Undefined
Pages (from-to)	309-315
Journal	Information processing letters
Volume	87
Issue number	6
DOIs	https://doi.org/10.1016/S0020-0190(03)00343-0
Publication status	Published - 2003

Keywords

IR-75030
Splay trees
Lumpability
Computational Complexity
Markov chains
Bisimulation

Access to Document

10.1016/S0020-0190(03)00343-0

Cite this

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title = "Optimal state-space lumping in Markov chains",

abstract = "We prove that the optimal lumping quotient of a finite Markov chain can be constructed in O(mlgn) time, where n is the number of states and m is the number of transitions. Our proof relies on the use of splay trees (designed by Sleator and Tarjan [J. ACM 32 (3) (1985) 652–686]) to sort transition weights.",

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AU - Hermanns, H.

AU - Sanders, William H.

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AB - We prove that the optimal lumping quotient of a finite Markov chain can be constructed in O(mlgn) time, where n is the number of states and m is the number of transitions. Our proof relies on the use of splay trees (designed by Sleator and Tarjan [J. ACM 32 (3) (1985) 652–686]) to sort transition weights.

KW - IR-75030

KW - Splay trees

KW - Lumpability

KW - Computational Complexity

KW - Markov chains

KW - Bisimulation

U2 - 10.1016/S0020-0190(03)00343-0

DO - 10.1016/S0020-0190(03)00343-0

M3 - Article

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SP - 309

EP - 315

JO - Information processing letters

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