The visual display of quantitative information
The visual display of quantitative information
Automatic average-case analysis of algorithms
Theoretical Computer Science - Theme issue on the algebraic and computing treatment of noncommutative power series
The art of computer programming, volume 1 (3rd ed.): fundamental algorithms
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IEEE Transactions on Pattern Analysis and Machine Intelligence
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The art of computer programming, volume 3: (2nd ed.) sorting and searching
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Foundations of statistical natural language processing
Foundations of statistical natural language processing
Probabilistic Languages: A Review and Some Open Questions
ACM Computing Surveys (CSUR)
The stack-size of tries: a combinatorial study
Theoretical Computer Science
Introduction To Automata Theory, Languages, And Computation
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Estimation of probabilistic context-free grammars
Computational Linguistics
Cross-entropy and estimation of probabilistic context-free grammars
HLT-NAACL '06 Proceedings of the main conference on Human Language Technology Conference of the North American Chapter of the Association of Computational Linguistics
Estimation of consistent probabilistic context-free grammars
HLT-NAACL '06 Proceedings of the main conference on Human Language Technology Conference of the North American Chapter of the Association of Computational Linguistics
Probabilistic Context-Free Grammars Estimated from Infinite Distributions
IEEE Transactions on Pattern Analysis and Machine Intelligence
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IEEE Transactions on Computers
Solution of an Open Problem on Probabilistic Grammars
IEEE Transactions on Computers
Analytic Combinatorics
On stochastic context-free languages
Information Sciences: an International Journal
New results on the size of tries
IEEE Transactions on Information Theory
Average case analysis of java 7's dual pivot quicksort
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
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We present a new approach for an average-case analysis of algorithms and data structures that supports a non-uniform distribution of the inputs and is based on the maximum likelihood training of stochastic grammars. The approach is exemplified by an analysis of the expected size of binary tries as well as by three sorting algorithms and it is compared to the known results that were obtained by traditional techniques. Investigating traditional settings like the random permutation model, we rediscover well-known results formerly derived by pure analytic methods; changing to biased data yields original results. All but one step of our analysis can be automated on top of a computer-algebra system. Thus our new approach can reduce the effort required for an average-case analysis, allowing for the consideration of realistic input distributions with unknown distribution functions at the same time. As a by-product, our approach yields an easy way to generate random combinatorial objects according to various probability distributions.