Suffix Tree of Alignment: An Efficient Index for Similar Data

We consider an index data structure for similar strings. The generalized suffix tree can be a solution for this. The generalized suffix tree of two strings $A$ and $B$ is a compacted trie representing all suffixes in $A$ and $B$. It has $|A|+|B|$ leaves and can be constructed in $O(|A|+|B|)$ time. However, if the two strings are similar, the generalized suffix tree is not efficient because it does not exploit the similarity which is usually represented as an alignment of $A$ and $B$. In this paper we propose a space/time-efficient suffix tree of alignment which wisely exploits the similarity in an alignment. Our suffix tree for an alignment of $A$ and $B$ has $|A| + l_d + l_1$ leaves where $l_d$ is the sum of the lengths of all parts of $B$ different from $A$ and $l_1$ is the sum of the lengths of some common parts of $A$ and $B$. We did not compromise the pattern search to reduce the space. Our suffix tree can be searched for a pattern $P$ in $O(|P|+occ)$ time where $occ$ is the number of occurrences of $P$ in $A$ and $B$. We also present an efficient algorithm to construct the suffix tree of alignment. When the suffix tree is constructed from scratch, the algorithm requires $O(|A| + l_d + l_1 + l_2)$ time where $l_2$ is the sum of the lengths of other common substrings of $A$ and $B$. When the suffix tree of $A$ is already given, it requires $O(l_d + l_1 + l_2)$ time.Comment: 12 page

Fast construction of FM-index for long sequence reads

Summary: We present a new method to incrementally construct the FM-index for both short and long sequence reads, up to the size of a genome. It is the first algorithm that can build the index while implicitly sorting the sequences in the reverse (complement) lexicographical order without a separate sorting step. The implementation is among the fastest for indexing short reads and the only one that practically works for reads of averaged kilobases in length. Availability and implementation: https://github.com/lh3/ropebwt2 Contact: [email protected]: 2 page

Accurate long read mapping using enhanced suffix arrays

With the rise of high throughput sequencing, new programs have been developed for dealing with the alignment of a huge amount of short read data to reference genomes. Recent developments in sequencing technology allow longer reads, but the mappers for short reads are not suited for reads of several hundreds of base pairs. We propose an algorithm for mapping longer reads, which is based on chaining maximal exact matches and uses heuristics and the Needleman-Wunsch algorithm to bridge the gaps. To compute maximal exact matches we use a specialized index structure, called enhanced suffix array. The proposed algorithm is very accurate and can handle large reads with mutations and long insertions and deletions

Fully-Functional Suffix Trees and Optimal Text Searching in BWT-runs Bounded Space

Indexing highly repetitive texts - such as genomic databases, software repositories and versioned text collections - has become an important problem since the turn of the millennium. A relevant compressibility measure for repetitive texts is r, the number of runs in their Burrows-Wheeler Transforms (BWTs). One of the earliest indexes for repetitive collections, the Run-Length FM-index, used O(r) space and was able to efficiently count the number of occurrences of a pattern of length m in the text (in loglogarithmic time per pattern symbol, with current techniques). However, it was unable to locate the positions of those occurrences efficiently within a space bounded in terms of r. In this paper we close this long-standing problem, showing how to extend the Run-Length FM-index so that it can locate the occ occurrences efficiently within O(r) space (in loglogarithmic time each), and reaching optimal time, O(m + occ), within O(r log log w ({\sigma} + n/r)) space, for a text of length n over an alphabet of size {\sigma} on a RAM machine with words of w = {\Omega}(log n) bits. Within that space, our index can also count in optimal time, O(m). Multiplying the space by O(w/ log {\sigma}), we support count and locate in O(dm log({\sigma})/we) and O(dm log({\sigma})/we + occ) time, which is optimal in the packed setting and had not been obtained before in compressed space. We also describe a structure using O(r log(n/r)) space that replaces the text and extracts any text substring of length ` in almost-optimal time O(log(n/r) + ` log({\sigma})/w). Within that space, we similarly provide direct access to suffix array, inverse suffix array, and longest common prefix array cells, and extend these capabilities to full suffix tree functionality, typically in O(log(n/r)) time per operation.Comment: submitted version; optimal count and locate in smaller space: O(r log log_w(n/r + sigma)

Parallel Suffix Tree Construction for Genome Sequence Using Hadoop

Indexing the genome is the basis for many of the bioinformatics applications. Read mapping (sequence alignment) is one such application to align millions of short reads against reference genome. Several tools like BLAST, SOAP, BOWTIE, Cloudburst, and Rapid Parallel Genome Indexing with MapReduce use indexing technique for aligning short reads. Many of the contemporary alignment techniques are time consuming, memory intensive and cannot be easily scaled to larger genomes. Suffix tree is a popular data structure which can be used to overcome the demerits of other alignment techniques. However, constructing the suffix tree is highly memory intensive and time consuming. In this thesis, a MapReduce based parallel construction of the suffix tree is proposed. The performance of the algorithm is measured on the hadoop framework over commodity cluster with each node having 8GB of primary memory. The results show a significantly less time for constructing suffix tree for a big data like human genome

Algoritmi za učinkovitu usporedbu sekvenci bez korištenja sravnjivanja

Sequence comparison is an essential tool in modern biology. It is used to identify homologous regions between sequences, and to detect evolutionary relationships between organisms. Sequence comparison is usually based on alignments. However, aligning whole genomes is computationally difficult. As an alternative approach, alignment-free sequence comparison can be used. In my thesis, I concentrate on two problems that can be solved without alignment: (i) estimation of substitution rates between nucleotide sequences, and (ii) detection of local sequence homology. In the first part of my thesis, I developed and implemented a new algorithm for the efficient alignment-free computation of the number of nucleotide substitutions per site, and applied it to the analysis of large data sets of complete genomes. In the second part of my thesis, I developed and implemented a new algorithm for detecting matching regions between nucleotide sequences. I applied this solution to the classification of circulating recombinant forms of HIV, and to the analysis of bacterial genomes subject to horizontal gene transfer.Table of Contents 1. GENERAL INTRODUCTION.........................................................................1 1.1. Suffix trees and other index data structures used in biological sequence analysis.....................................................................................................................9 1.1.1. Suffix Tree..........................................................................................11 1.1.2. The space and the time complexity of the algorithms for the suffix tree construction.......................................................................................................13 1.1.3. Suffix Array........................................................................................14 1.1.4. The space and the time complexity of the algorithms for suffix array construction.......................................................................................................15 1.1.5. Enhanced Suffix Array.......................................................................17 1.1.6. The 64-bit implementation of the lightweight suffix array construction algorithm 21 1.1.7. Self-index...........................................................................................22 1.1.8. Burrows-Wheeler transform..............................................................23 1.1.9. The FM-Index and the backward search algorithm..........................25 1.1.10. The space and the time-complexity of the FM-index.........................29 2. EFFICIENT ESTIMATION OF PAIRWISE DISTANCES BETWEEN GENOMES...............................................................................................................31 2.1. Introduction................................................................................................31 2.2. Methods.....................................................................................................33 2.2.1. Definition of an alignment-free estimator of the rate of substitution, Kr 33 2.2.2. Problem statement.............................................................................35 2.2.3. Time complexity analysis of the previous approach (kr 1)................35 2.2.4. Time complexity analysis of the new approach (kr 2).......................37 2.2.5. Algorithm 1: Computation of all Kr values during the traversal of a generalized suffix tree of n sequences................................................................38 2.2.6. The implementation of kr version 2...................................................44 2.3. Analysis of Kr on simulated data sets........................................................45 2.3.1. Auxiliary programs............................................................................45 2.3.2. Consistency of Kr...............................................................................46 i 2.3.3. The affect of horizontal gene transfer on the accuracy of Kr............48 2.3.4. The effect of genome duplication on the accuracy of Kr....................49 2.3.5. Run time comparison of kr 1 and kr 2...............................................50 2.4. Application of kr version 2........................................................................53 2.4.1. Auxililary software used for the analysis of real data sets................56 2.4.2. The analysis of 12 Drosophila genomes............................................57 2.4.3. The analysis of 13 Escherichia coli and Shigella genomes...............58 2.4.4. The analysis of 825 HIV-1 pure subtype genomes.............................61 2.5. Discussion..................................................................................................62 3. EFFICIENT ALIGNMENT-FREE DETECTION OF LOCAL SEQUENCE HOMOLOGY....................................................................................66 3.1. Introduction................................................................................................66 3.2. Methods.....................................................................................................69 3.2.1. Problem statement – determining subtype(s) of a query sequence....69 3.2.2. Construction of locally homologous segments..................................71 3.2.3. Time complexity of computing a list of intervals Ii............................72 3.2.4. Algorithm 2: Construction of an interval tree...................................73 3.2.5. Computing a list of segements Gi.......................................................80 3.3. Analysis of st on simulated data sets.........................................................82 3.3.1. Run-time and memory usage analysis of st........................................82 3.3.2. Consistency of st................................................................................85 3.3.3. Comparison to SCUEAL on simulated data sets...............................92 3.4. Application of st.........................................................................................97 3.4.1. The analysis of Neisseria meningitidis..............................................98 3.4.2. The analysis of a recombinant form of HIV-1...................................99 3.4.3. The analysis of circulating recombinant forms of HIV-1................103 3.4.4. The analysis of an avian pathogenic Escherichia coli strain..........104 3.5. Discussion................................................................................................107 4. CONCLUSION..............................................................................................110 5. REFERENCES..............................................................................................112 6. ELECTRONIC SOURCES...........................................................................121 7. LIST OF ABBREVIATIONS AND SYMBOLS.........................................122 ii iii ABSTRACT............................................................................................................124 SAŽETAK..............................................................................................................125 CURRICULUM VITAE........................................................................................126 ŽIVOTOPIS...........................................................................................................12

A new method for indexing genomes using on-disk suffix trees

We propose a new method to build persistent suffix trees for indexing the genomic data. Our algorithm DiGeST (Disk-Based Genomic Suffix Tree) improves significantly over previous work in reducing the random access to the in-put string and performing only two passes over disk data. DiGeST is based on the two-phase multi-way merge sort paradigm using a concise binary representation of the DNA alphabet. Furthermore, our method scales to larger genomic data than managed before