Average-case analysis of programs: Automated recurrence analysis for almost-linear bounds

1 Anonymous, 2 Anonymous, 3 Anonymous, Average-Case Analysis of Programs: Automated Recurrence Analysis for Almost-Linear Bounds, IST Austria, 2016.

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Technical Report | Published | English
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IST Austria Technical Report
Abstract
We consider the problem of developing automated techniques to aid the average-case complexity analysis of programs. Several classical textbook algorithms have quite efficient average-case complexity, whereas the corresponding worst-case bounds are either inefficient (e.g., QUICK-SORT), or completely ineffective (e.g., COUPONCOLLECTOR). Since the main focus of average-case 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 size of the input). Our main contribution is a sound approach for deriving such average-case bounds for randomized recursive programs. Our approach is efficient (a simple linear-time algorithm), and it is based on (a) the analysis of recurrence relations induced by randomized algorithms, and (b) a guess-and-check technique. Our approach can infer the asymptotically optimal average-case bounds for classical randomized algorithms, including RANDOMIZED-SEARCH, QUICKSORT, QUICK-SELECT, COUPON-COLLECTOR, where the worstcase bounds are either inefficient (such as linear as compared to logarithmic of average-case, or quadratic as compared to linear or almost-linear of average-case), or ineffective. We have implemented our approach, and the experimental results show that we obtain the bounds efficiently for various classical algorithms.
Publishing Year
Date Published
2016-07-15
Page
20
ISSN
IST-REx-ID

Cite this

Anonymous 1, Anonymous 2, Anonymous 3. Average-Case Analysis of Programs: Automated Recurrence Analysis for Almost-Linear Bounds. IST Austria; 2016.
Anonymous, 1, Anonymous, 2, & Anonymous, 3. (2016). Average-case analysis of programs: Automated recurrence analysis for almost-linear bounds. IST Austria.
Anonymous, 1, 2 Anonymous, and 3 Anonymous. Average-Case Analysis of Programs: Automated Recurrence Analysis for Almost-Linear Bounds. IST Austria, 2016.
1 Anonymous, 2 Anonymous, and 3 Anonymous, Average-case analysis of programs: Automated recurrence analysis for almost-linear bounds. IST Austria, 2016.
Anonymous 1, Anonymous 2, Anonymous 3. 2016. Average-case analysis of programs: Automated recurrence analysis for almost-linear bounds, IST Austria, 20p.
Anonymous, 1, et al. Average-Case Analysis of Programs: Automated Recurrence Analysis for Almost-Linear Bounds. IST Austria, 2016.
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