{"type":"technical_report","publication_status":"published","ddc":["000"],"file":[{"file_id":"5482","access_level":"open_access","date_created":"2018-12-12T11:53:21Z","file_size":1089651,"date_updated":"2020-07-14T12:46:52Z","checksum":"62c6ea01e342553dcafb88a070fb1ad5","creator":"system","file_name":"IST-2015-319-v1+1_long.pdf","relation":"main_file","content_type":"application/pdf"}],"publisher":"IST Austria","citation":{"ista":"Chatterjee K, Ibsen-Jensen R, Pavlogiannis A. 2015. Faster algorithms for quantitative verification in constant treewidth graphs, IST Austria, 31p.","mla":"Chatterjee, Krishnendu, et al. <i>Faster Algorithms for Quantitative Verification in Constant Treewidth Graphs</i>. IST Austria, 2015, doi:<a href=\"https://doi.org/10.15479/AT:IST-2015-319-v1-1\">10.15479/AT:IST-2015-319-v1-1</a>.","ama":"Chatterjee K, Ibsen-Jensen R, Pavlogiannis A. <i>Faster Algorithms for Quantitative Verification in Constant Treewidth Graphs</i>. IST Austria; 2015. doi:<a href=\"https://doi.org/10.15479/AT:IST-2015-319-v1-1\">10.15479/AT:IST-2015-319-v1-1</a>","chicago":"Chatterjee, Krishnendu, Rasmus Ibsen-Jensen, and Andreas Pavlogiannis. <i>Faster Algorithms for Quantitative Verification in Constant Treewidth Graphs</i>. IST Austria, 2015. <a href=\"https://doi.org/10.15479/AT:IST-2015-319-v1-1\">https://doi.org/10.15479/AT:IST-2015-319-v1-1</a>.","apa":"Chatterjee, K., Ibsen-Jensen, R., &#38; Pavlogiannis, A. (2015). <i>Faster algorithms for quantitative verification in constant treewidth graphs</i>. IST Austria. <a href=\"https://doi.org/10.15479/AT:IST-2015-319-v1-1\">https://doi.org/10.15479/AT:IST-2015-319-v1-1</a>","ieee":"K. Chatterjee, R. Ibsen-Jensen, and A. Pavlogiannis, <i>Faster algorithms for quantitative verification in constant treewidth graphs</i>. IST Austria, 2015.","short":"K. Chatterjee, R. Ibsen-Jensen, A. Pavlogiannis, Faster Algorithms for Quantitative Verification in Constant Treewidth Graphs, IST Austria, 2015."},"month":"02","related_material":{"record":[{"id":"1607","status":"public","relation":"later_version"},{"id":"5437","status":"public","relation":"later_version"}]},"department":[{"_id":"KrCh"}],"abstract":[{"lang":"eng","text":"We consider the core algorithmic problems related to verification of systems with respect to three classical quantitative properties, namely, the mean- payoff property, the ratio property, and the minimum initial credit for energy property. The algorithmic problem given a graph and a quantitative property asks to compute the optimal value (the infimum value over all traces) from every node of the graph. We consider graphs with constant treewidth, and it is well-known that the control-flow graphs of most programs have constant treewidth. Let n denote the number of nodes of a graph, m the number of edges (for constant treewidth graphs m = O ( n ) ) and W the largest absolute value of the weights. Our main theoretical results are as follows. First, for constant treewidth graphs we present an algorithm that approximates the mean-payoff value within a mul- tiplicative factor of ∊ in time O ( n · log( n/∊ )) and linear space, as compared to the classical algorithms that require quadratic time. Second, for the ratio property we present an algorithm that for constant treewidth graphs works in time O ( n · log( | a · b · n | )) = O ( n · log( n · W )) , when the output is a b , as compared to the previously best known algorithm with running time O ( n 2 · log( n · W )) . Third, for the minimum initial credit problem we show that (i) for general graphs the problem can be solved in O ( n 2 · m ) time and the associated decision problem can be solved in O ( n · m ) time, improving the previous known O ( n 3 · m · log( n · W )) and O ( n 2 · m ) bounds, respectively; and (ii) for constant treewidth graphs we present an algorithm that requires O ( n · log n ) time, improving the previous known O ( n 4 · log( n · W )) bound. We have implemented some of our algorithms and show that they present a significant speedup on standard benchmarks."}],"status":"public","oa":1,"date_published":"2015-02-10T00:00:00Z","oa_version":"Published Version","author":[{"first_name":"Krishnendu","orcid":"0000-0002-4561-241X","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","last_name":"Chatterjee","full_name":"Chatterjee, Krishnendu"},{"id":"3B699956-F248-11E8-B48F-1D18A9856A87","last_name":"Ibsen-Jensen","orcid":"0000-0003-4783-0389","first_name":"Rasmus","full_name":"Ibsen-Jensen, Rasmus"},{"full_name":"Pavlogiannis, Andreas","last_name":"Pavlogiannis","orcid":"0000-0002-8943-0722","id":"49704004-F248-11E8-B48F-1D18A9856A87","first_name":"Andreas"}],"publication_identifier":{"issn":["2664-1690"]},"pubrep_id":"319","file_date_updated":"2020-07-14T12:46:52Z","date_updated":"2023-02-23T12:26:22Z","has_accepted_license":"1","language":[{"iso":"eng"}],"date_created":"2018-12-12T11:39:17Z","title":"Faster algorithms for quantitative verification in constant treewidth graphs","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","page":"31","_id":"5430","year":"2015","day":"10","doi":"10.15479/AT:IST-2015-319-v1-1","alternative_title":["IST Austria Technical Report"]}