{"volume":10426,"date_updated":"2021-01-12T08:06:55Z","type":"conference","publication_identifier":{"isbn":["978-331963386-2"]},"conference":{"name":"CAV: Computer Aided Verification","location":"Heidelberg, Germany","end_date":"2017-07-28","start_date":"2017-07-24"},"author":[{"full_name":"Chatterjee, Krishnendu","first_name":"Krishnendu","orcid":"0000-0002-4561-241X","last_name":"Chatterjee","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Hongfei","full_name":"Fu, Hongfei","last_name":"Fu"},{"full_name":"Murhekar, Aniket","first_name":"Aniket","last_name":"Murhekar"}],"doi":"10.1007/978-3-319-63387-9_6","_id":"628","alternative_title":["LNCS"],"publication_status":"published","abstract":[{"lang":"eng","text":"We consider the problem of developing automated techniques for solving recurrence relations to aid the expected-runtime analysis of programs. The motivation is that several classical textbook algorithms have quite efficient expected-runtime complexity, whereas the corresponding worst-case bounds are either inefficient (e.g., Quick-Sort), or completely ineffective (e.g., Coupon-Collector). Since the main focus of expected-runtime analysis is to obtain efficient bounds, we consider bounds that are either logarithmic, linear or almost-linear (O(log n), O(n), O(n · log n), respectively, where n represents the input size). Our main contribution is an efficient (simple linear-time algorithm) sound approach for deriving such expected-runtime bounds for the analysis of recurrence relations induced by randomized algorithms. The experimental results show that our approach can efficiently derive asymptotically optimal expected-runtime bounds for recurrences of classical randomized algorithms, including Randomized-Search, Quick-Sort, Quick-Select, Coupon-Collector, where the worst-case bounds are either inefficient (such as linear as compared to logarithmic expected-runtime complexity, or quadratic as compared to linear or almost-linear expected-runtime complexity), or ineffective."}],"department":[{"_id":"KrCh"}],"citation":{"ama":"Chatterjee K, Fu H, Murhekar A. Automated recurrence analysis for almost linear expected runtime bounds. In: Majumdar R, Kunčak V, eds. Vol 10426. Springer; 2017:118-139. doi:<a href=\"https://doi.org/10.1007/978-3-319-63387-9_6\">10.1007/978-3-319-63387-9_6</a>","mla":"Chatterjee, Krishnendu, et al. <i>Automated Recurrence Analysis for Almost Linear Expected Runtime Bounds</i>. Edited by Rupak Majumdar and Viktor Kunčak, vol. 10426, Springer, 2017, pp. 118–39, doi:<a href=\"https://doi.org/10.1007/978-3-319-63387-9_6\">10.1007/978-3-319-63387-9_6</a>.","short":"K. Chatterjee, H. Fu, A. Murhekar, in:, R. Majumdar, V. Kunčak (Eds.), Springer, 2017, pp. 118–139.","ieee":"K. Chatterjee, H. Fu, and A. Murhekar, “Automated recurrence analysis for almost linear expected runtime bounds,” presented at the CAV: Computer Aided Verification, Heidelberg, Germany, 2017, vol. 10426, pp. 118–139.","chicago":"Chatterjee, Krishnendu, Hongfei Fu, and Aniket Murhekar. “Automated Recurrence Analysis for Almost Linear Expected Runtime Bounds.” edited by Rupak Majumdar and Viktor Kunčak, 10426:118–39. Springer, 2017. <a href=\"https://doi.org/10.1007/978-3-319-63387-9_6\">https://doi.org/10.1007/978-3-319-63387-9_6</a>.","ista":"Chatterjee K, Fu H, Murhekar A. 2017. Automated recurrence analysis for almost linear expected runtime bounds. CAV: Computer Aided Verification, LNCS, vol. 10426, 118–139.","apa":"Chatterjee, K., Fu, H., &#38; Murhekar, A. (2017). Automated recurrence analysis for almost linear expected runtime bounds. In R. Majumdar &#38; V. Kunčak (Eds.) (Vol. 10426, pp. 118–139). Presented at the CAV: Computer Aided Verification, Heidelberg, Germany: Springer. <a href=\"https://doi.org/10.1007/978-3-319-63387-9_6\">https://doi.org/10.1007/978-3-319-63387-9_6</a>"},"date_created":"2018-12-11T11:47:35Z","month":"01","page":"118 - 139","project":[{"grant_number":"ICT15-003","_id":"25892FC0-B435-11E9-9278-68D0E5697425","name":"Efficient Algorithms for Computer Aided Verification"},{"name":"Game Theory","call_identifier":"FWF","grant_number":"S11407","_id":"25863FF4-B435-11E9-9278-68D0E5697425"},{"_id":"2581B60A-B435-11E9-9278-68D0E5697425","grant_number":"279307","call_identifier":"FP7","name":"Quantitative Graph Games: Theory and Applications"}],"status":"public","user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","oa":1,"publist_id":"7166","intvolume":"     10426","language":[{"iso":"eng"}],"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1705.00314"}],"title":"Automated recurrence analysis for almost linear expected runtime bounds","quality_controlled":"1","scopus_import":1,"oa_version":"Submitted Version","ec_funded":1,"publisher":"Springer","year":"2017","day":"01","date_published":"2017-01-01T00:00:00Z","editor":[{"last_name":"Majumdar","first_name":"Rupak","full_name":"Majumdar, Rupak"},{"first_name":"Viktor","full_name":"Kunčak, Viktor","last_name":"Kunčak"}]}