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Full Compressed Affix Tree Representations L.I.R.M.M. Universit e - - PowerPoint PPT Presentation
Full Compressed Affix Tree Representations L.I.R.M.M. Universit e - - PowerPoint PPT Presentation
Full Compressed Affix Tree Representations L.I.R.M.M. Universit e de Montpellier Institut Biologie Computationnelle Introduction Basic Concepts A Classification Asynchronous Approaches Synchronous Approaches Results Conclusions &
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Motivation
Bidirectional Search Example: Harpins
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Introduction Basic Concepts A Classification Asynchronous Approaches Synchronous Approaches Results Conclusions & Future Work
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Suffix Tree
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Suffix Tree Operations
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Suffix Arrays and Suffix Tree
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Suffix Arrays and Suffix Tree
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Burrows and Wheeler Transform (BWT)
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BWT: backward search
backwardSearch(c, [i, j]): i′ ← C[c] + Occ(c, i − 1) + 1 j′ ← C[c] + Occ(c, j)
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Affix Tree
◮ Combines Suffix Tree of T with the Suffix Tree T r ◮ Introduced by Stoye (2000) and Maaß (2003) ◮ Problem: Complexity of the structures presented and that it
uses about 45n bytes
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Introduction Basic Concepts A Classification Asynchronous Approaches Synchronous Approaches Results Conclusions & Future Work
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Asynchronous vs Synchronous
◮ Forward Structure (FOS) and the Backward Structure (BAS)
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Introduction Basic Concepts A Classification Asynchronous Approaches Synchronous Approaches Results Conclusions & Future Work
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Affix Array (AfA)
◮ Proposed by Strothmann (2007) ◮ Suffix Trees are stored using Suffix Arrays in addition with
extra data
◮ Connections between the trees are also stored (Affix links) ◮ Does not support all tree operations ◮ Total: around 18–22n bytes.
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Compressed Affix Tree (ACAT)
◮ Compressed Suffix Trees data structure ◮ Supports all tree operations ◮ Connections between the trees are also stored (Affix links)
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Affix Link
ALink(v) = Child(Alink(SLink(v)), c)
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Affix Link
ALink(v) = Child(Alink(SLink(v)), c)
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Affix Link
ALink(v) = Child(Alink(SLink(v)), c)
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Sampled Affix Link
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Compressed Affix Tree Sampled (ACATS)
◮ Compressed Suffix Trees data structure ◮ Sampled Affix links
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Compressed Affix Tree Non-Sampled
◮ Extreme case ACATS ◮ Albrecht and Heun (2012). Optimal computation of Affix
links using binary search
◮ Gog et al. (2014). Faster solution (ACATN)
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ACATN
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ACATN
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RACATN
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Introduction Basic Concepts A Classification Asynchronous Approaches Synchronous Approaches Results Conclusions & Future Work
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Bidirectional Wavelet Tree (BidWT)
◮ Proposed by Schnattinger et al. (2010 − 2012) and Lam et al.
(2009)
◮ Uses backward index for the input text T and for T r ◮ Easy transition between the data structures ◮ Reduce space in a factor of 23 compared to the Affix Array ◮ Main operation: extend in one character
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Bidirectional Wavelet Tree
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Bidirectional Wavelet Tree
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Bidirectional Wavelet Tree
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SCAT
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SCAT
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Summary
Approach Category Full Tree Description Operations Space AfA Asynchronous No Strothmann’s Affix Array 2 · (SA + LCP + child tables + ALink) ACAT Asynchronous Yes Asynchronous Affix Tree implementation 2 · (CST + ALink) ACATS Asynchronous Yes Asynchronous Affix Tree implementation 2 · (CST + Alinksampled) ACATN Asynchronous Yes Gog et al. Affix Tree 2 · (CST + rminq + rmaxq) RACATN Asynchronous Yes reduced of ACATN 2 · (CST + rminq) BidWT Synchronous No Bidirectional BWT 2 · (FM-Index) SCAT Synchronous Yes Synchronous Affix Tree implementation 2 · (CST)
Table: Compressed Affix Tree approaches studied in this work.
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Introduction Basic Concepts A Classification Asynchronous Approaches Synchronous Approaches Results Conclusions & Future Work
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Construction
DNA-50MB ENGLISH-50MB
10000 100000 1e+06 1e+07 1 10 100 Time in milliseconds Number of bytes per character AFA ACAT ACATS ACATN RACATN BidWT SCAT 10000 100000 1e+06 1e+07 1 10 100 Time in milliseconds Number of bytes per character AFA ACAT ACATS ACATN RACATN BidWT SCAT
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Forward-Backward
DNA-50MB ENGLISH-50MB
0.1 1 10 100 1 10 100 Time in microseconds Number of bytes per character AFA ACAT ACATS ACATN RACATN BidWT SCAT 1 10 100 1 10 100 Time in microseconds Number of bytes per character AFA ACAT ACATS ACATN RACATN BidWT SCAT
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Suffix-Children
DNA-50MB ENGLISH-50MB
1 10 100 1000 1 10 100 Time in microseconds Number of bytes per character AFA ACAT ACATS ACATN RACATN BidWT SCAT 1 10 100 1000 1 10 100 Time in microseconds Number of bytes per character AFA ACAT ACATS ACATN RACATN BidWT SCAT
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Slink
DNA-50MB ENGLISH-50MB
10 100 1 10 100 Time in microseconds Number of bytes per character ACAT ACATS ACATN RACATN SCAT 1 10 100 1 10 100 Time in microseconds Number of bytes per character ACAT ACATS ACATN RACATN SCAT
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Introduction Basic Concepts A Classification Asynchronous Approaches Synchronous Approaches Results Conclusions & Future Work
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