Faster and dynamic algorithms for maximal end component decomposition and related graph problems in probabilistic verification

K. Chatterjee, M. Henzinger, in:, SIAM, 2011, pp. 1318–1336.


Conference Paper | Published | English
Author
Department
Abstract
We present faster and dynamic algorithms for the following problems arising in probabilistic verification: Computation of the maximal end-component (mec) decomposition of Markov decision processes (MDPs), and of the almost sure winning set for reachability and parity objectives in MDPs. We achieve the following running time for static algorithms in MDPs with graphs of n vertices and m edges: (1) O(m · min{ √m, n2/3 }) for the mec decomposition, improving the longstanding O(m·n) bound; (2) O(m·n2/3) for reachability objectives, improving the previous O(m · √m) bound for m > n4/3; and (3) O(m · min{ √m, n2/3 } · log(d)) for parity objectives with d priorities, improving the previous O(m · √m · d) bound. We also give incremental and decremental algorithms in linear time for mec decomposition and reachability objectives and O(m · log d) time for parity ob jectives.
Publishing Year
Date Published
2011-01-01
Page
1318 - 1336
Conference
SODA: Symposium on Discrete Algorithms
Conference Location
San Francisco, USA
Conference Date
2011-01-23 – 2011-01-25
IST-REx-ID

Cite this

Chatterjee K, Henzinger M. Faster and dynamic algorithms for maximal end component decomposition and related graph problems in probabilistic verification. In: SIAM; 2011:1318-1336. doi:10.1137/1.9781611973082.101
Chatterjee, K., & Henzinger, M. (2011). Faster and dynamic algorithms for maximal end component decomposition and related graph problems in probabilistic verification (pp. 1318–1336). Presented at the SODA: Symposium on Discrete Algorithms, San Francisco, USA: SIAM. https://doi.org/10.1137/1.9781611973082.101
Chatterjee, Krishnendu, and Monika Henzinger. “Faster and Dynamic Algorithms for Maximal End Component Decomposition and Related Graph Problems in Probabilistic Verification,” 1318–36. SIAM, 2011. https://doi.org/10.1137/1.9781611973082.101.
K. Chatterjee and M. Henzinger, “Faster and dynamic algorithms for maximal end component decomposition and related graph problems in probabilistic verification,” presented at the SODA: Symposium on Discrete Algorithms, San Francisco, USA, 2011, pp. 1318–1336.
Chatterjee K, Henzinger M. 2011. Faster and dynamic algorithms for maximal end component decomposition and related graph problems in probabilistic verification. SODA: Symposium on Discrete Algorithms 1318–1336.
Chatterjee, Krishnendu, and Monika Henzinger. Faster and Dynamic Algorithms for Maximal End Component Decomposition and Related Graph Problems in Probabilistic Verification. SIAM, 2011, pp. 1318–36, doi:10.1137/1.9781611973082.101.

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