{"oa":1,"status":"public","abstract":[{"text":"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 &gt; 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.","lang":"eng"}],"conference":{"name":"SODA: Symposium on Discrete Algorithms","end_date":"2011-01-25","start_date":"2011-01-23","location":"San Francisco, SA, United States"},"date_published":"2011-01-01T00:00:00Z","oa_version":"Submitted Version","department":[{"_id":"KrCh"}],"main_file_link":[{"open_access":"1","url":"https://eprints.cs.univie.ac.at/21/"}],"scopus_import":"1","month":"01","publisher":"SIAM","citation":{"short":"K. Chatterjee, M.H. Henzinger, in:, SIAM, 2011, pp. 1318–1336.","ieee":"K. Chatterjee and M. H. 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, SA, United States, 2011, pp. 1318–1336.","ama":"Chatterjee K, Henzinger MH. Faster and dynamic algorithms for maximal end-component decomposition and related graph problems in probabilistic verification. In: SIAM; 2011:1318-1336. doi:<a href=\"https://doi.org/10.1137/1.9781611973082.101\">10.1137/1.9781611973082.101</a>","chicago":"Chatterjee, Krishnendu, and Monika H Henzinger. “Faster and Dynamic Algorithms for Maximal End-Component Decomposition and Related Graph Problems in Probabilistic Verification,” 1318–36. SIAM, 2011. <a href=\"https://doi.org/10.1137/1.9781611973082.101\">https://doi.org/10.1137/1.9781611973082.101</a>.","apa":"Chatterjee, K., &#38; Henzinger, M. H. (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, SA, United States: SIAM. <a href=\"https://doi.org/10.1137/1.9781611973082.101\">https://doi.org/10.1137/1.9781611973082.101</a>","mla":"Chatterjee, Krishnendu, and Monika H. Henzinger. <i>Faster and Dynamic Algorithms for Maximal End-Component Decomposition and Related Graph Problems in Probabilistic Verification</i>. SIAM, 2011, pp. 1318–36, doi:<a href=\"https://doi.org/10.1137/1.9781611973082.101\">10.1137/1.9781611973082.101</a>.","ista":"Chatterjee K, Henzinger MH. 2011. Faster and dynamic algorithms for maximal end-component decomposition and related graph problems in probabilistic verification. SODA: Symposium on Discrete Algorithms, 1318–1336."},"type":"conference","publist_id":"3278","publication_status":"published","quality_controlled":"1","doi":"10.1137/1.9781611973082.101","page":"1318 - 1336","year":"2011","day":"01","_id":"3343","article_processing_charge":"No","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","title":"Faster and dynamic algorithms for maximal end-component decomposition and related graph problems in probabilistic verification","author":[{"orcid":"0000-0002-4561-241X","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","last_name":"Chatterjee","first_name":"Krishnendu","full_name":"Chatterjee, Krishnendu"},{"full_name":"Henzinger, Monika H","first_name":"Monika H","id":"540c9bbd-f2de-11ec-812d-d04a5be85630","orcid":"0000-0002-5008-6530","last_name":"Henzinger"}],"date_created":"2018-12-11T12:02:47Z","date_updated":"2023-02-14T10:36:10Z","language":[{"iso":"eng"}]}