Geometric Burrows-Wheeler Transform: Linking Range Searching and Text Indexing

Chien, Yu-Feng; Hon, Wing-Kai; Shah, Rahul; Vitter, Jeffrey Scott

doi:10.1109/dcc.2008.67

Cited by 51 publications

(37 citation statements)

References 15 publications

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“…Our range search structure is an improvement upon that of Mäkinen and Navarro [15], and we use it to improve previous results on designing space-efficient text indexes for substring search [7] and position-restricted substring search [15]. We also apply our structure to extend the previous result on representing a sequence of small integers succinctly [10], as well as a restricted version of orthogonal range search in which the query range is defined by two points in the point set [4].…”

Section: Our Resultsmentioning

confidence: 82%

“…A succinct text index of O(n lg σ) bits for a text string T of length n over an alphabet of size σ that supports substring search in O(m + lg n(lg σ n + occ lg n)/ lg lg n) time, where m is the length of the query substring, and occ is the number of its occurrences in T . This provides faster query support than the structure of Chien et al [7] while using the same amounts of space. 3.…”

Section: Our Resultsmentioning

confidence: 96%

“…Our data structure not only can be used as a key component in solutions to the general orthogonal range search problem to save storage cost, but also has applications in text indexing. In particular, we apply it to improve two previous space-efficient text indexes that support substring search [7] and position-restricted substring search [15]. We also use it to extend previous results on succinct representations of sequences of small integers, and to design succinct data structures supporting certain types of orthogonal range query in the plane.…”

mentioning

confidence: 99%

“…They showed how to reduce the problem to orthogonal range search on an n × n grid, and designed a text index of 3n lg n + o(n lg n) bits to support position-restricted substring search in O(m + occ lg n) time, where occ is the number of occurrences of P in T . Chien et al [7] considered the problem of indexing a text string to support the general substring search that reports the occurrences of a query pattern P in a text string T . This is a fundamental problem in computer science.…”

Section: Introductionmentioning

confidence: 99%

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Succinct Orthogonal Range Search Structures on a Grid with Applications to Text Indexing

Bose

Maheshwari

et al. 2009

Lecture Notes in Computer Science

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Abstract. We present a succinct representation of a set of n points on an n × n grid using n lg n + o(n lg n) bits 3 to support orthogonal range counting in O(lg n/ lg lg n) time, and range reporting in O(k lg n/ lg lg n) time, where k is the size of the output. This achieves an improvement on query time by a factor of lg lg n upon the previous result of Mäkinen and Navarro [15], while using essentially the information-theoretic minimum space. Our data structure not only can be used as a key component in solutions to the general orthogonal range search problem to save storage cost, but also has applications in text indexing. In particular, we apply it to improve two previous space-efficient text indexes that support substring search [7] and position-restricted substring search [15]. We also use it to extend previous results on succinct representations of sequences of small integers, and to design succinct data structures supporting certain types of orthogonal range query in the plane.

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Section: Our Resultsmentioning

confidence: 82%

Section: Our Resultsmentioning

confidence: 96%

mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Succinct Orthogonal Range Search Structures on a Grid with Applications to Text Indexing

Bose

Maheshwari

et al. 2009

Lecture Notes in Computer Science

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“…Specified meta-characters should then be located on the text to finalize the actual search (see [17] for detailed analysis of the case), which is not so elegant.…”

Section: Introductionmentioning

confidence: 99%

Ψ-RA: a parallel sparse index for genomic read alignment

Külekçi¹,

Hon

Shah

et al. 2011

BMC Genomics

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BackgroundGenomic read alignment involves mapping (exactly or approximately) short reads from a particular individual onto a pre-sequenced reference genome of the same species. Because all individuals of the same species share the majority of their genomes, short reads alignment provides an alternative and much more efficient way to sequence the genome of a particular individual than does direct sequencing. Among many strategies proposed for this alignment process, indexing the reference genome and short read searching over the index is a dominant technique. Our goal is to design a space-efficient indexing structure with fast searching capability to catch the massive short reads produced by the next generation high-throughput DNA sequencing technology.ResultsWe concentrate on indexing DNA sequences via sparse suffix arrays (SSAs) and propose a new short read aligner named Ψ-RA (PSI-RA: parallel sparse index read aligner). The motivation in using SSAs is the ability to trade memory against time. It is possible to fine tune the space consumption of the index based on the available memory of the machine and the minimum length of the arriving pattern queries. Although SSAs have been studied before for exact matching of short reads, an elegant way of approximate matching capability was missing. We provide this by defining the rightmost mismatch criteria that prioritize the errors towards the end of the reads, where errors are more probable. Ψ-RA supports any number of mismatches in aligning reads. We give comparisons with some of the well-known short read aligners, and show that indexing a genome with SSA is a good alternative to the Burrows-Wheeler transform or seed-based solutions.ConclusionsΨ-RA is expected to serve as a valuable tool in the alignment of short reads generated by the next generation high-throughput sequencing technology. Ψ-RA is very fast in exact matching and also supports rightmost approximate matching. The SSA structure that Ψ-RA is built on naturally incorporates the modern multicore architecture and thus further speed-up can be gained. All the information, including the source code of Ψ-RA, can be downloaded at: http://www.busillis.com/o_kulekci/PSIRA.zip.

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Succinct and I/O Efficient Data Structures for Traversal in Trees

Dillabaugh

Maheshwari

2008

Algorithms and Computation

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Abstract. We present two results for path traversal in trees, where the traversal is performed in an asymptotically optimal number of I/Os and the tree structure is represented succinctly. Our first result is for bottom-up traversal that starts with a node in a tree on N nodes and traverses a path to the root. For a bottom-up path of length K, we design data structures that permit traversal of this path in O(K/B) I/Os (B denotes the size of a disk block) using only 2N + ǫN log B N + o(N ) bits, for an arbitrarily selected constant, ǫ, where 0 < ǫ < 1. Our second result is for top-down traversal in binary trees. We store the tree in (3 + q)N + o(N ) bits, where q is the number of bits required to store a key, while top-down traversal can still be performed in an asymptotically optimal number of I/Os.

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Geometric Burrows-Wheeler Transform: Linking Range Searching and Text Indexing

Cited by 51 publications

References 15 publications

Succinct Orthogonal Range Search Structures on a Grid with Applications to Text Indexing

Succinct Orthogonal Range Search Structures on a Grid with Applications to Text Indexing

Ψ-RA: a parallel sparse index for genomic read alignment

Succinct and I/O Efficient Data Structures for Traversal in Trees

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