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- W4300650557 abstract "We consider the problem of developing automated techniques for solving recurrence relations to aid the expected-runtime analysis of programs. 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 ($mathcal{O}(log n)$, $mathcal{O}(n)$, $mathcal{O}(ncdotlog n)$, 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. Our approach can infer the asymptotically optimal expected-runtime bounds for recurrences of classical randomized algorithms, including RANDOMIZED-SEARCH, QUICK-SORT, QUICK-SELECT, COUPONCOLLECTOR, where the worst-case bounds are either inefficient (such as linear as compared to logarithmic of expected-runtime, or quadratic as compared to linear or almost-linear of expected-runtime), or ineffective. We have implemented our approach, and the experimental results show that we obtain the bounds efficiently for the recurrences of various classical algorithms." @default.
- W4300650557 created "2022-10-03" @default.
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- W4300650557 date "2017-04-30" @default.
- W4300650557 modified "2023-10-16" @default.
- W4300650557 title "Automated Recurrence Analysis for Almost-Linear Expected-Runtime Bounds" @default.
- W4300650557 doi "https://doi.org/10.48550/arxiv.1705.00314" @default.
- W4300650557 hasPublicationYear "2017" @default.
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