[{"language":[{"iso":"eng"}],"doi":"10.4230/LIPIcs.MFCS.2017.61","ddc":["004"],"citation":{"ama":"Chatterjee K, Ibsen-Jensen R, Nowak M. Faster Monte Carlo algorithms for fixation probability of the Moran process on undirected graphs. In: <i>Leibniz International Proceedings in Informatics</i>. Vol 83. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2017. doi:<a href=\"https://doi.org/10.4230/LIPIcs.MFCS.2017.61\">10.4230/LIPIcs.MFCS.2017.61</a>","apa":"Chatterjee, K., Ibsen-Jensen, R., &#38; Nowak, M. (2017). Faster Monte Carlo algorithms for fixation probability of the Moran process on undirected graphs. In <i>Leibniz International Proceedings in Informatics</i> (Vol. 83). Aalborg, Denmark: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. <a href=\"https://doi.org/10.4230/LIPIcs.MFCS.2017.61\">https://doi.org/10.4230/LIPIcs.MFCS.2017.61</a>","short":"K. Chatterjee, R. Ibsen-Jensen, M. Nowak, in:, Leibniz International Proceedings in Informatics, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2017.","mla":"Chatterjee, Krishnendu, et al. “Faster Monte Carlo Algorithms for Fixation Probability of the Moran Process on Undirected Graphs.” <i>Leibniz International Proceedings in Informatics</i>, vol. 83, 61, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2017, doi:<a href=\"https://doi.org/10.4230/LIPIcs.MFCS.2017.61\">10.4230/LIPIcs.MFCS.2017.61</a>.","chicago":"Chatterjee, Krishnendu, Rasmus Ibsen-Jensen, and Martin Nowak. “Faster Monte Carlo Algorithms for Fixation Probability of the Moran Process on Undirected Graphs.” In <i>Leibniz International Proceedings in Informatics</i>, Vol. 83. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2017. <a href=\"https://doi.org/10.4230/LIPIcs.MFCS.2017.61\">https://doi.org/10.4230/LIPIcs.MFCS.2017.61</a>.","ista":"Chatterjee K, Ibsen-Jensen R, Nowak M. 2017. Faster Monte Carlo algorithms for fixation probability of the Moran process on undirected graphs. Leibniz International Proceedings in Informatics. MFCS: Mathematical Foundations of Computer Science (SG), LIPIcs, vol. 83, 61.","ieee":"K. Chatterjee, R. Ibsen-Jensen, and M. Nowak, “Faster Monte Carlo algorithms for fixation probability of the Moran process on undirected graphs,” in <i>Leibniz International Proceedings in Informatics</i>, Aalborg, Denmark, 2017, vol. 83."},"title":"Faster Monte Carlo algorithms for fixation probability of the Moran process on undirected graphs","conference":{"location":"Aalborg, Denmark","start_date":"2017-08-21","end_date":"2017-08-25","name":"MFCS: Mathematical Foundations of Computer Science (SG)"},"day":"01","type":"conference","author":[{"orcid":"0000-0002-4561-241X","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","first_name":"Krishnendu","full_name":"Chatterjee, Krishnendu","last_name":"Chatterjee"},{"full_name":"Ibsen-Jensen, Rasmus","first_name":"Rasmus","last_name":"Ibsen-Jensen","orcid":"0000-0003-4783-0389","id":"3B699956-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Nowak","full_name":"Nowak, Martin","first_name":"Martin"}],"alternative_title":["LIPIcs"],"publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","publication":"Leibniz International Proceedings in Informatics","quality_controlled":"1","department":[{"_id":"KrCh"}],"status":"public","intvolume":"        83","month":"11","date_created":"2018-12-11T11:47:08Z","scopus_import":1,"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","date_updated":"2021-01-12T08:02:34Z","publication_identifier":{"isbn":["978-395977046-0"]},"publist_id":"7263","year":"2017","has_accepted_license":"1","oa_version":"Published Version","publication_status":"published","oa":1,"file_date_updated":"2020-07-14T12:47:00Z","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)"},"pubrep_id":"924","volume":83,"file":[{"file_id":"5322","relation":"main_file","content_type":"application/pdf","date_created":"2018-12-12T10:18:04Z","file_size":535077,"creator":"system","file_name":"IST-2018-924-v1+1_LIPIcs-MFCS-2017-61.pdf","access_level":"open_access","date_updated":"2020-07-14T12:47:00Z","checksum":"2eed5224c0e4e259484a1d71acb8ba6a"}],"article_number":"61","_id":"551","date_published":"2017-11-01T00:00:00Z","abstract":[{"text":"Evolutionary graph theory studies the evolutionary dynamics in a population structure given as a connected graph. Each node of the graph represents an individual of the population, and edges determine how offspring are placed. We consider the classical birth-death Moran process where there are two types of individuals, namely, the residents with fitness 1 and mutants with fitness r. The fitness indicates the reproductive strength. The evolutionary dynamics happens as follows: in the initial step, in a population of all resident individuals a mutant is introduced, and then at each step, an individual is chosen proportional to the fitness of its type to reproduce, and the offspring replaces a neighbor uniformly at random. The process stops when all individuals are either residents or mutants. The probability that all individuals in the end are mutants is called the fixation probability, which is a key factor in the rate of evolution. We consider the problem of approximating the fixation probability. The class of algorithms that is extremely relevant for approximation of the fixation probabilities is the Monte-Carlo simulation of the process. Previous results present a polynomial-time Monte-Carlo algorithm for undirected graphs when r is given in unary. First, we present a simple modification: instead of simulating each step, we discard ineffective steps, where no node changes type (i.e., either residents replace residents, or mutants replace mutants). Using the above simple modification and our result that the number of effective steps is concentrated around the expected number of effective steps, we present faster polynomial-time Monte-Carlo algorithms for undirected graphs. Our algorithms are always at least a factor O(n2/ log n) faster as compared to the previous algorithms, where n is the number of nodes, and is polynomial even if r is given in binary. We also present lower bounds showing that the upper bound on the expected number of effective steps we present is asymptotically tight for undirected graphs. ","lang":"eng"}]},{"license":"https://creativecommons.org/licenses/by/3.0/","publication_status":"published","oa":1,"file_date_updated":"2020-07-14T12:47:00Z","volume":83,"tmp":{"short":"CC BY (3.0)","legal_code_url":"https://creativecommons.org/licenses/by/3.0/legalcode","name":"Creative Commons Attribution 3.0 Unported (CC BY 3.0)","image":"/images/cc_by.png"},"pubrep_id":"923","article_processing_charge":"No","file":[{"file_size":610339,"creator":"system","file_name":"IST-2018-923-v1+1_LIPIcs-MFCS-2017-39.pdf","checksum":"c67f4866ddbfd555afef1f63ae9a8fc7","access_level":"open_access","date_updated":"2020-07-14T12:47:00Z","relation":"main_file","file_id":"5248","content_type":"application/pdf","date_created":"2018-12-12T10:16:57Z"}],"article_number":"39","abstract":[{"lang":"eng","text":"Graph games provide the foundation for modeling and synthesis of reactive processes. Such games are played over graphs where the vertices are controlled by two adversarial players. We consider graph games where the objective of the first player is the conjunction of a qualitative objective (specified as a parity condition) and a quantitative objective (specified as a meanpayoff condition). There are two variants of the problem, namely, the threshold problem where the quantitative goal is to ensure that the mean-payoff value is above a threshold, and the value problem where the quantitative goal is to ensure the optimal mean-payoff value; in both cases ensuring the qualitative parity objective. The previous best-known algorithms for game graphs with n vertices, m edges, parity objectives with d priorities, and maximal absolute reward value W for mean-payoff objectives, are as follows: O(nd+1 . m . w) for the threshold problem, and O(nd+2 · m · W) for the value problem. Our main contributions are faster algorithms, and the running times of our algorithms are as follows: O(nd-1 · m ·W) for the threshold problem, and O(nd · m · W · log(n · W)) for the value problem. For mean-payoff parity objectives with two priorities, our algorithms match the best-known bounds of the algorithms for mean-payoff games (without conjunction with parity objectives). Our results are relevant in synthesis of reactive systems with both functional requirement (given as a qualitative objective) and performance requirement (given as a quantitative objective)."}],"_id":"552","date_published":"2017-11-01T00:00:00Z","date_updated":"2023-02-14T10:06:46Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","scopus_import":"1","publication_identifier":{"isbn":["978-395977046-0"]},"publist_id":"7262","oa_version":"Published Version","has_accepted_license":"1","year":"2017","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","department":[{"_id":"KrCh"}],"quality_controlled":"1","publication":"Leibniz International Proceedings in Informatics","intvolume":"        83","status":"public","month":"11","date_created":"2018-12-11T11:47:08Z","project":[{"grant_number":"S11407","name":"Game Theory","call_identifier":"FWF","_id":"25863FF4-B435-11E9-9278-68D0E5697425"},{"call_identifier":"FP7","_id":"2581B60A-B435-11E9-9278-68D0E5697425","grant_number":"279307","name":"Quantitative Graph Games: Theory and Applications"}],"language":[{"iso":"eng"}],"doi":"10.4230/LIPIcs.MFCS.2017.39","ddc":["004"],"ec_funded":1,"citation":{"ista":"Chatterjee K, Henzinger MH, Svozil A. 2017. Faster algorithms for mean-payoff parity games. Leibniz International Proceedings in Informatics. MFCS: Mathematical Foundations of Computer Science (SG), LIPIcs, vol. 83, 39.","ieee":"K. Chatterjee, M. H. Henzinger, and A. Svozil, “Faster algorithms for mean-payoff parity games,” in <i>Leibniz International Proceedings in Informatics</i>, Aalborg, Denmark, 2017, vol. 83.","chicago":"Chatterjee, Krishnendu, Monika H Henzinger, and Alexander Svozil. “Faster Algorithms for Mean-Payoff Parity Games.” In <i>Leibniz International Proceedings in Informatics</i>, Vol. 83. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2017. <a href=\"https://doi.org/10.4230/LIPIcs.MFCS.2017.39\">https://doi.org/10.4230/LIPIcs.MFCS.2017.39</a>.","mla":"Chatterjee, Krishnendu, et al. “Faster Algorithms for Mean-Payoff Parity Games.” <i>Leibniz International Proceedings in Informatics</i>, vol. 83, 39, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2017, doi:<a href=\"https://doi.org/10.4230/LIPIcs.MFCS.2017.39\">10.4230/LIPIcs.MFCS.2017.39</a>.","short":"K. Chatterjee, M.H. Henzinger, A. Svozil, in:, Leibniz International Proceedings in Informatics, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2017.","apa":"Chatterjee, K., Henzinger, M. H., &#38; Svozil, A. (2017). Faster algorithms for mean-payoff parity games. In <i>Leibniz International Proceedings in Informatics</i> (Vol. 83). Aalborg, Denmark: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. <a href=\"https://doi.org/10.4230/LIPIcs.MFCS.2017.39\">https://doi.org/10.4230/LIPIcs.MFCS.2017.39</a>","ama":"Chatterjee K, Henzinger MH, Svozil A. Faster algorithms for mean-payoff parity games. In: <i>Leibniz International Proceedings in Informatics</i>. Vol 83. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2017. doi:<a href=\"https://doi.org/10.4230/LIPIcs.MFCS.2017.39\">10.4230/LIPIcs.MFCS.2017.39</a>"},"conference":{"location":"Aalborg, Denmark","end_date":"2017-08-25","start_date":"2017-08-21","name":"MFCS: Mathematical Foundations of Computer Science (SG)"},"title":"Faster algorithms for mean-payoff parity games","day":"01","alternative_title":["LIPIcs"],"type":"conference","author":[{"id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4561-241X","last_name":"Chatterjee","full_name":"Chatterjee, Krishnendu","first_name":"Krishnendu"},{"first_name":"Monika H","full_name":"Henzinger, Monika H","last_name":"Henzinger","orcid":"0000-0002-5008-6530","id":"540c9bbd-f2de-11ec-812d-d04a5be85630"},{"last_name":"Svozil","first_name":"Alexander","full_name":"Svozil, Alexander"}]},{"date_created":"2018-12-11T11:47:08Z","month":"11","status":"public","intvolume":"        83","publication":"Leibniz International Proceedings in Informatics","department":[{"_id":"KrCh"}],"quality_controlled":"1","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","author":[{"id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4561-241X","first_name":"Krishnendu","full_name":"Chatterjee, Krishnendu","last_name":"Chatterjee"},{"first_name":"Kristofer","full_name":"Hansen, Kristofer","last_name":"Hansen"},{"id":"3B699956-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-4783-0389","last_name":"Ibsen-Jensen","full_name":"Ibsen-Jensen, Rasmus","first_name":"Rasmus"}],"type":"conference","alternative_title":["LIPIcs"],"day":"01","title":"Strategy complexity of concurrent safety games","conference":{"location":"Aalborg, Denmark","name":"MFCS: Mathematical Foundations of Computer Science (SG)","start_date":"2017-08-21","end_date":"2017-08-25"},"citation":{"ama":"Chatterjee K, Hansen K, Ibsen-Jensen R. Strategy complexity of concurrent safety games. In: <i>Leibniz International Proceedings in Informatics</i>. Vol 83. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2017. doi:<a href=\"https://doi.org/10.4230/LIPIcs.MFCS.2017.55\">10.4230/LIPIcs.MFCS.2017.55</a>","apa":"Chatterjee, K., Hansen, K., &#38; Ibsen-Jensen, R. (2017). Strategy complexity of concurrent safety games. In <i>Leibniz International Proceedings in Informatics</i> (Vol. 83). Aalborg, Denmark: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. <a href=\"https://doi.org/10.4230/LIPIcs.MFCS.2017.55\">https://doi.org/10.4230/LIPIcs.MFCS.2017.55</a>","short":"K. Chatterjee, K. Hansen, R. Ibsen-Jensen, in:, Leibniz International Proceedings in Informatics, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2017.","mla":"Chatterjee, Krishnendu, et al. “Strategy Complexity of Concurrent Safety Games.” <i>Leibniz International Proceedings in Informatics</i>, vol. 83, 55, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2017, doi:<a href=\"https://doi.org/10.4230/LIPIcs.MFCS.2017.55\">10.4230/LIPIcs.MFCS.2017.55</a>.","chicago":"Chatterjee, Krishnendu, Kristofer Hansen, and Rasmus Ibsen-Jensen. “Strategy Complexity of Concurrent Safety Games.” In <i>Leibniz International Proceedings in Informatics</i>, Vol. 83. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2017. <a href=\"https://doi.org/10.4230/LIPIcs.MFCS.2017.55\">https://doi.org/10.4230/LIPIcs.MFCS.2017.55</a>.","ieee":"K. Chatterjee, K. Hansen, and R. Ibsen-Jensen, “Strategy complexity of concurrent safety games,” in <i>Leibniz International Proceedings in Informatics</i>, Aalborg, Denmark, 2017, vol. 83.","ista":"Chatterjee K, Hansen K, Ibsen-Jensen R. 2017. Strategy complexity of concurrent safety games. Leibniz International Proceedings in Informatics. MFCS: Mathematical Foundations of Computer Science (SG), LIPIcs, vol. 83, 55."},"ddc":["004"],"doi":"10.4230/LIPIcs.MFCS.2017.55","language":[{"iso":"eng"}],"date_published":"2017-11-01T00:00:00Z","_id":"553","abstract":[{"text":"We consider two player, zero-sum, finite-state concurrent reachability games, played for an infinite number of rounds, where in every round, each player simultaneously and independently of the other players chooses an action, whereafter the successor state is determined by a probability distribution given by the current state and the chosen actions. Player 1 wins iff a designated goal state is eventually visited. We are interested in the complexity of stationary strategies measured by their patience, which is defined as the inverse of the smallest non-zero probability employed. Our main results are as follows: We show that: (i) the optimal bound on the patience of optimal and -optimal strategies, for both players is doubly exponential; and (ii) even in games with a single non-absorbing state exponential (in the number of actions) patience is necessary. ","lang":"eng"}],"file":[{"date_created":"2018-12-12T10:09:29Z","file_id":"4753","relation":"main_file","content_type":"application/pdf","access_level":"open_access","date_updated":"2020-07-14T12:47:00Z","checksum":"7101facb56ade363205c695d72dbd173","creator":"system","file_size":549967,"file_name":"IST-2018-922-v1+1_LIPIcs-MFCS-2017-55.pdf"}],"article_number":"55","pubrep_id":"922","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)"},"volume":83,"file_date_updated":"2020-07-14T12:47:00Z","main_file_link":[{"url":"https://arxiv.org/abs/1506.02434","open_access":"1"}],"oa":1,"publication_status":"published","has_accepted_license":"1","year":"2017","oa_version":"Published Version","publist_id":"7261","publication_identifier":{"isbn":["978-395977046-0"]},"scopus_import":1,"date_updated":"2021-01-12T08:02:35Z","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87"}]