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240
Fast and accurate short read alignment with BurrowsWheeler transform
 BIOINFORMATICS, 2009, ADVANCE ACCESS
, 2009
"... Motivation: The enormous amount of short reads generated by the new DNA sequencing technologies call for the development of fast and accurate read alignment programs. A first generation of hashtable based methods has been developed, including MAQ, which is accurate, feature rich and fast enough to a ..."
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Cited by 2043 (22 self)
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Motivation: The enormous amount of short reads generated by the new DNA sequencing technologies call for the development of fast and accurate read alignment programs. A first generation of hashtable based methods has been developed, including MAQ, which is accurate, feature rich and fast enough to align short reads from a single individual. However, MAQ does not support gapped alignment for singleend reads, which makes it unsuitable for alignment of longer reads where indels may occur frequently. The speed of MAQ is also a concern when the alignment is scaled up to the resequencing of hundreds of individuals. Results: We implemented BWA, a new read alignment package that is based on backward search with BurrowsWheeler Transform (BWT), to efficiently align short sequencing reads against a large reference sequence such as the human genome, allowing mismatches and gaps. BWA supports both base space reads, e.g. from Illumina sequencing machines, and color space reads from AB SOLiD machines. Evaluations on both simulated and real data suggest that BWA is ∼10–20X faster than MAQ while achieving similar accuracy. In addition, BWA outputs alignment in the new standard SAM format. Variant calling and other downstream analyses after the alignment can be achieved with the opensource SAMtools software package.
Opportunistic Data Structures with Applications
, 2000
"... In this paper we address the issue of compressing and indexing data. We devise a data structure whose space occupancy is a function of the entropy of the underlying data set. We call the data structure opportunistic since its space occupancy is decreased when the input is compressible and this space ..."
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Cited by 290 (11 self)
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In this paper we address the issue of compressing and indexing data. We devise a data structure whose space occupancy is a function of the entropy of the underlying data set. We call the data structure opportunistic since its space occupancy is decreased when the input is compressible and this space reduction is achieved at no significant slowdown in the query performance. More precisely, its space occupancy is optimal in an informationcontent sense because a text T [1, u] is stored using O(H k (T )) + o(1) bits per input symbol in the worst case, where H k (T ) is the kth order empirical entropy of T (the bound holds for any fixed k). Given an arbitrary string P [1; p], the opportunistic data structure allows to search for the occ occurrences of P in T in O(p + occ log u) time (for any fixed > 0). If data are uncompressible we achieve the best space bound currently known [12]; on compressible data our solution improves the succinct suffix array of [12] and the classical suffix tree and suffix array data structures either in space or in query time or both.
Highorder entropycompressed text indexes
, 2003
"... We present a novel implementation of compressed suffix arrays exhibiting new tradeoffs between search time and space occupancy for a given text (or sequence) of n symbols over an alphabet Σ, where each symbol is encoded by lg Σ  bits. We show that compressed suffix arrays use just nHh + O(n lg lg ..."
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Cited by 275 (22 self)
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We present a novel implementation of compressed suffix arrays exhibiting new tradeoffs between search time and space occupancy for a given text (or sequence) of n symbols over an alphabet Σ, where each symbol is encoded by lg Σ  bits. We show that compressed suffix arrays use just nHh + O(n lg lg n / lg Σ  n) bits, while retaining full text indexing functionalities, such as searching any pattern sequence of length m in O(m lg Σ  + polylog(n)) time. The term Hh ≤ lg Σ  denotes the hthorder empirical entropy of the text, which means that our index is nearly optimal in space apart from lowerorder terms, achieving asymptotically the empirical entropy of the text (with a multiplicative constant 1). If the text is highly compressible so that Hh = o(1) and the alphabet size is small, we obtain a text index with o(m) search time that requires only o(n) bits. Further results and tradeoffs are reported in the paper. 1
Compressed fulltext indexes
 ACM COMPUTING SURVEYS
, 2007
"... Fulltext indexes provide fast substring search over large text collections. A serious problem of these indexes has traditionally been their space consumption. A recent trend is to develop indexes that exploit the compressibility of the text, so that their size is a function of the compressed text l ..."
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Cited by 269 (97 self)
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Fulltext indexes provide fast substring search over large text collections. A serious problem of these indexes has traditionally been their space consumption. A recent trend is to develop indexes that exploit the compressibility of the text, so that their size is a function of the compressed text length. This concept has evolved into selfindexes, which in addition contain enough information to reproduce any text portion, so they replace the text. The exciting possibility of an index that takes space close to that of the compressed text, replaces it, and in addition provides fast search over it, has triggered a wealth of activity and produced surprising results in a very short time, and radically changed the status of this area in less than five years. The most successful indexes nowadays are able to obtain almost optimal space and search time simultaneously. In this paper we present the main concepts underlying selfindexes. We explain the relationship between text entropy and regularities that show up in index structures and permit compressing them. Then we cover the most relevant selfindexes up to date, focusing on the essential aspects on how they exploit the text compressibility and how they solve efficiently various search problems. We aim at giving the theoretical background to understand and follow the developments in this area.
Succinct indexable dictionaries with applications to encoding kary trees and multisets
 In Proceedings of the 13th Annual ACMSIAM Symposium on Discrete Algorithms (SODA
"... We consider the indexable dictionary problem, which consists of storing a set S ⊆ {0,...,m − 1} for some integer m, while supporting the operations of rank(x), which returns the number of elements in S that are less than x if x ∈ S, and −1 otherwise; and select(i) which returns the ith smallest ele ..."
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Cited by 266 (14 self)
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We consider the indexable dictionary problem, which consists of storing a set S ⊆ {0,...,m − 1} for some integer m, while supporting the operations of rank(x), which returns the number of elements in S that are less than x if x ∈ S, and −1 otherwise; and select(i) which returns the ith smallest element in S. We give a data structure that supports both operations in O(1) time on the RAM model and requires B(n,m)+ o(n)+O(lg lg m) bits to store a set of size n, where B(n,m) = ⌈ lg ( m) ⌉ n is the minimum number of bits required to store any nelement subset from a universe of size m. Previous dictionaries taking this space only supported (yes/no) membership queries in O(1) time. In the cell probe model we can remove the O(lg lg m) additive term in the space bound, answering a question raised by Fich and Miltersen, and Pagh. We present extensions and applications of our indexable dictionary data structure, including: • an informationtheoretically optimal representation of a kary cardinal tree that supports standard operations in constant time, • a representation of a multiset of size n from {0,...,m − 1} in B(n,m+n) + o(n) bits that supports (appropriate generalizations of) rank and select operations in constant time, and • a representation of a sequence of n nonnegative integers summing up to m in B(n,m + n) + o(n) bits that supports prefix sum queries in constant time. 1
Indexing compressed text
, 2005
"... We design two compressed data structures for the fulltext indexing problem that support efficient substring searches using roughly the space required for storing the text in compressed form. Our first compressed data structure retrieves the occ occurrences of a pattern P[1, p] within a text T [1, ..."
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Cited by 173 (14 self)
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We design two compressed data structures for the fulltext indexing problem that support efficient substring searches using roughly the space required for storing the text in compressed form. Our first compressed data structure retrieves the occ occurrences of a pattern P[1, p] within a text T [1, n] inO(p + occ log 1+ɛ n) time for any chosen ɛ, 0<ɛ<1. This data structure uses at most 5nHk(T)+o(n) bits of storage, where Hk(T)isthekth order empirical entropy of T. The space usage is �(n) bits in the worst case and o(n) bits for compressible texts. This data structure exploits the relationship between suffix arrays and the Burrows–Wheeler Transform, and can be regarded as a compressed suffix array. Our second compressed data structure achieves O(p + occ) query time using O(nHk(T) log ɛ n)+ o(n) bits of storage for any chosen ɛ, 0<ɛ<1. Therefore, it provides optimal outputsensitive query time using o(n log n) bits in the worst case. This second data structure builds upon the first one and exploits the interplay between two compressors: the Burrows–Wheeler Transform and theLZ78 algorithm.
Compressed representations of sequences and fulltext indexes
 ACM Transactions on Algorithms
, 2007
"... Abstract. Given a sequence S = s1s2... sn of integers smaller than r = O(polylog(n)), we show how S can be represented using nH0(S) + o(n) bits, so that we can know any sq, as well as answer rank and select queries on S, in constant time. H0(S) is the zeroorder empirical entropy of S and nH0(S) pro ..."
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Cited by 162 (79 self)
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Abstract. Given a sequence S = s1s2... sn of integers smaller than r = O(polylog(n)), we show how S can be represented using nH0(S) + o(n) bits, so that we can know any sq, as well as answer rank and select queries on S, in constant time. H0(S) is the zeroorder empirical entropy of S and nH0(S) provides an Information Theoretic lower bound to the bit storage of any sequence S via a fixed encoding of its symbols. This extends previous results on binary sequences, and improves previous results on general sequences where those queries are answered in O(log r) time. For larger r, we can still represent S in nH0(S) + o(n log r) bits and answer queries in O(log r / log log n) time. Another contribution of this paper is to show how to combine our compressed representation of integer sequences with an existing compression boosting technique to design compressed fulltext indexes that scale well with the size of the input alphabet Σ. Namely, we design a variant of the FMindex that indexes a string T [1, n] within nHk(T) + o(n) bits of storage, where Hk(T) is the kth order empirical entropy of T. This space bound holds simultaneously for all k ≤ α log Σ  n, constant 0 < α < 1, and Σ  = O(polylog(n)). This index counts the occurrences of an arbitrary pattern P [1, p] as a substring of T in O(p) time; it locates each pattern occurrence in O(log 1+ε n) time, for any constant 0 < ε < 1; and it reports a text substring of length ℓ in O(ℓ + log 1+ε n) time.
Lineartime longestcommonprefix computation in suffix arrays and its applications
, 2001
"... Abstract. We present a lineartime algorithm to compute the longest common prefix information in suffix arrays. As two applications of our algorithm, we show that our algorithm is crucial to the effective use of blocksorting compression, and we present a lineartime algorithm to simulate the bottom ..."
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Cited by 113 (2 self)
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Abstract. We present a lineartime algorithm to compute the longest common prefix information in suffix arrays. As two applications of our algorithm, we show that our algorithm is crucial to the effective use of blocksorting compression, and we present a lineartime algorithm to simulate the bottomup traversal of a suffix tree with a suffix array combined with the longest common prefix information. 1
Compressed suffix trees with full functionality
 Theory of Computing Systems
"... We introduce new data structures for compressed suffix trees whose size are linear in the text size. The size is measured in bits; thus they occupy only O(n log A) bits for a text of length n on an alphabet A. This is a remarkable improvement on current suffix trees which require O(n log n) bits. ..."
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Cited by 86 (6 self)
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We introduce new data structures for compressed suffix trees whose size are linear in the text size. The size is measured in bits; thus they occupy only O(n log A) bits for a text of length n on an alphabet A. This is a remarkable improvement on current suffix trees which require O(n log n) bits. Though some components of suffix trees have been compressed, there is no linearsize data structure for suffix trees with full functionality such as computing suffix links, stringdepths and lowest common ancestors. The data structure proposed in this paper is the first one that has linear size and supports all operations efficiently. Any algorithm running on a suffix tree can also be executed on our compressed suffix trees with a slight slowdown of a factor of polylog(n). 1
Dictionary Matching and Indexing with Errors and Don't Cares
 In Proceedings of STOC
, 2004
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