{"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","page":"27","related_material":{"record":[{"id":"1607","status":"public","relation":"later_version"},{"relation":"earlier_version","status":"public","id":"5430"}]},"department":[{"_id":"KrCh"}],"file_date_updated":"2020-07-14T12:46:54Z","language":[{"iso":"eng"}],"author":[{"id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","last_name":"Chatterjee","full_name":"Chatterjee, Krishnendu","first_name":"Krishnendu","orcid":"0000-0002-4561-241X"},{"full_name":"Ibsen-Jensen, Rasmus","orcid":"0000-0003-4783-0389","first_name":"Rasmus","last_name":"Ibsen-Jensen","id":"3B699956-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Pavlogiannis, Andreas","orcid":"0000-0002-8943-0722","first_name":"Andreas","last_name":"Pavlogiannis","id":"49704004-F248-11E8-B48F-1D18A9856A87"}],"ddc":["000"],"year":"2015","file":[{"date_created":"2018-12-12T11:53:12Z","file_name":"IST-2015-330-v2+1_main.pdf","file_size":1072137,"content_type":"application/pdf","date_updated":"2020-07-14T12:46:54Z","relation":"main_file","access_level":"open_access","file_id":"5473","creator":"system","checksum":"f5917c20f84018b362d385c000a2e123"}],"day":"27","date_published":"2015-04-27T00:00:00Z","alternative_title":["IST Austria Technical Report"],"date_updated":"2023-02-23T12:26:05Z","date_created":"2018-12-12T11:39:19Z","status":"public","abstract":[{"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. \r\nThe 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.\r\nOur main theoretical results are as follows.\r\nFirst, for constant treewidth graphs we present an algorithm that approximates the mean-payoff value within a multiplicative factor of $\\epsilon$ in time $O(n \\cdot \\log (n/\\epsilon))$ 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 $O(n \\cdot \\log (|a\\cdot b|))=O(n\\cdot\\log (n\\cdot W))$, when the output is $\\frac{a}{b}$, as compared to the previously best known algorithm with running time $O(n^2 \\cdot \\log (n\\cdot W))$. Third, for the minimum initial credit problem we show that (i)~for general graphs the problem can be solved in $O(n^2\\cdot m)$ time and the associated decision problem can be solved in $O(n\\cdot m)$ time, improving the previous known $O(n^3\\cdot m\\cdot \\log (n\\cdot W))$ and $O(n^2 \\cdot m)$ bounds, respectively; and (ii)~for constant treewidth graphs we present an algorithm that requires $O(n\\cdot \\log n)$ time, improving the previous known $O(n^4 \\cdot \\log (n \\cdot W))$ bound.\r\nWe have implemented some of our algorithms and show that they present a significant speedup on standard benchmarks. ","lang":"eng"}],"oa_version":"Published Version","type":"technical_report","citation":{"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-2015-330-v2-1\">https://doi.org/10.15479/AT:IST-2015-330-v2-1</a>","short":"K. Chatterjee, R. Ibsen-Jensen, A. Pavlogiannis, Faster Algorithms for Quantitative Verification in Constant Treewidth Graphs, IST Austria, 2015.","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-2015-330-v2-1\">10.15479/AT:IST-2015-330-v2-1</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-2015-330-v2-1\">https://doi.org/10.15479/AT:IST-2015-330-v2-1</a>.","ieee":"K. Chatterjee, R. Ibsen-Jensen, and A. Pavlogiannis, <i>Faster algorithms for quantitative verification in constant treewidth graphs</i>. IST Austria, 2015.","ista":"Chatterjee K, Ibsen-Jensen R, Pavlogiannis A. 2015. Faster algorithms for quantitative verification in constant treewidth graphs, IST Austria, 27p.","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-2015-330-v2-1\">10.15479/AT:IST-2015-330-v2-1</a>"},"_id":"5437","has_accepted_license":"1","doi":"10.15479/AT:IST-2015-330-v2-1","publication_identifier":{"issn":["2664-1690"]},"title":"Faster algorithms for quantitative verification in constant treewidth graphs","month":"04","pubrep_id":"333","publication_status":"published","publisher":"IST Austria","oa":1}