Chatterjee, KrishnenduISTA ; Fu, Hongfei; Murhekar, Aniket
Majumdar, Rupak; Kunčak, Viktor
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.
118 - 139
CAV: Computer Aided Verification
2017-07-24 – 2017-07-28
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:10.1007/978-3-319-63387-9_6
Chatterjee, K., Fu, H., & Murhekar, A. (2017). Automated recurrence analysis for almost linear expected runtime bounds. In R. Majumdar & V. Kunčak (Eds.) (Vol. 10426, pp. 118–139). Presented at the CAV: Computer Aided Verification, Heidelberg, Germany: Springer. https://doi.org/10.1007/978-3-319-63387-9_6
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. https://doi.org/10.1007/978-3-319-63387-9_6.
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.
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.
Chatterjee, Krishnendu, et al. Automated Recurrence Analysis for Almost Linear Expected Runtime Bounds. Edited by Rupak Majumdar and Viktor Kunčak, vol. 10426, Springer, 2017, pp. 118–39, doi:10.1007/978-3-319-63387-9_6.