Analysis of the average depth in a suffix tree under a Markov model
Julien Fayolle,Mark Daniel Ward +1 more
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TLDR
In this article, it was shown that under a Markovian model of order one, the average depth of suffix trees of index n is asymptotically similar to the average depths of tries (a.k.a. digital trees) built on n independent strings.Abstract:
In this report, we prove that under a Markovian model of order one, the average depth of suffix trees of index n is asymptotically similar to the average depth of tries (a.k.a. digital trees) built on n independent strings. This leads to an asymptotic behavior of $(\log{n})/h + C$ for the average of the depth of the suffix tree, where $h$ is the entropy of the Markov model and $C$ is constant. Our proof compares the generating functions for the average depth in tries and in suffix trees; the difference between these generating functions is shown to be asymptotically small. We conclude by using the asymptotic behavior of the average depth in a trie under the Markov model found by Jacquet and Szpankowski ([JaSz91]).read more
Citations
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Efficient Periodicity Mining in Time Series Databases Using Suffix Trees
TL;DR: This paper presents an algorithm which can detect symbol, sequence (partial), and segment (full cycle) periodicity in time series and is noise resilient; it is generally more time-efficient and noise-resilient than existing algorithms.
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A Framework for Periodic Outlier Pattern Detection in Time-Series Sequences
Faraz Rasheed,Reda Alhajj +1 more
TL;DR: This paper presents a robust and time efficient suffix tree-based algorithm capable of detecting the periodicity of outlier patterns in a time series by giving more significance to less frequent yet periodic patterns.
Journal ArticleDOI
Profiles of Tries
TL;DR: A detailed study of the distribution of the profiles in a trie built over random strings generated by a memoryless source finds typical behaviors of the height, shortest path, fill-up level, and depth.
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Analytic Pattern Matching
TL;DR: This book for researchers and graduate students demonstrates the probabilistic approach to pattern matching, which predicts the performance of pattern matching algorithms with very high precision using analytic combinatorics and analytic information theory.
Book ChapterDOI
Profile of tries
TL;DR: This work presents a detailed study of the distribution of the profiles in a trie built over strings generated by a memoryless source (extension to Markov sources is possible).
References
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