1,703 research outputs found
Dynamic Data Structures for Document Collections and Graphs
In the dynamic indexing problem, we must maintain a changing collection of
text documents so that we can efficiently support insertions, deletions, and
pattern matching queries. We are especially interested in developing efficient
data structures that store and query the documents in compressed form. All
previous compressed solutions to this problem rely on answering rank and select
queries on a dynamic sequence of symbols. Because of the lower bound in
[Fredman and Saks, 1989], answering rank queries presents a bottleneck in
compressed dynamic indexing. In this paper we show how this lower bound can be
circumvented using our new framework. We demonstrate that the gap between
static and dynamic variants of the indexing problem can be almost closed. Our
method is based on a novel framework for adding dynamism to static compressed
data structures. Our framework also applies more generally to dynamizing other
problems. We show, for example, how our framework can be applied to develop
compressed representations of dynamic graphs and binary relations
Succinct Representations of Dynamic Strings
The rank and select operations over a string of length n from an alphabet of
size have been used widely in the design of succinct data structures.
In many applications, the string itself need be maintained dynamically,
allowing characters of the string to be inserted and deleted. Under the word
RAM model with word size , we design a succinct representation
of dynamic strings using bits to support rank,
select, insert and delete in time. When the alphabet size is small, i.e. when \sigma = O(\polylog
(n)), including the case in which the string is a bit vector, these operations
are supported in time. Our data structures are more
efficient than previous results on the same problem, and we have applied them
to improve results on the design and construction of space-efficient text
indexes
Indexing large genome collections on a PC
Motivation: The availability of thousands of invidual genomes of one species
should boost rapid progress in personalized medicine or understanding of the
interaction between genotype and phenotype, to name a few applications. A key
operation useful in such analyses is aligning sequencing reads against a
collection of genomes, which is costly with the use of existing algorithms due
to their large memory requirements.
Results: We present MuGI, Multiple Genome Index, which reports all
occurrences of a given pattern, in exact and approximate matching model,
against a collection of thousand(s) genomes. Its unique feature is the small
index size fitting in a standard computer with 16--32\,GB, or even 8\,GB, of
RAM, for the 1000GP collection of 1092 diploid human genomes. The solution is
also fast. For example, the exact matching queries are handled in average time
of 39\,s and with up to 3 mismatches in 373\,s on the test PC with
the index size of 13.4\,GB. For a smaller index, occupying 7.4\,GB in memory,
the respective times grow to 76\,s and 917\,s.
Availability: Software and Suuplementary material:
\url{http://sun.aei.polsl.pl/mugi}
On the Benefit of Merging Suffix Array Intervals for Parallel Pattern Matching
We present parallel algorithms for exact and approximate pattern matching
with suffix arrays, using a CREW-PRAM with processors. Given a static text
of length , we first show how to compute the suffix array interval of a
given pattern of length in
time for . For approximate pattern matching with differences or
mismatches, we show how to compute all occurrences of a given pattern in
time, where is the size of the alphabet
and . The workhorse of our algorithms is a data structure
for merging suffix array intervals quickly: Given the suffix array intervals
for two patterns and , we present a data structure for computing the
interval of in sequential time, or in
parallel time. All our data structures are of size bits (in addition to
the suffix array)
A Faster Implementation of Online Run-Length Burrows-Wheeler Transform
Run-length encoding Burrows-Wheeler Transformed strings, resulting in
Run-Length BWT (RLBWT), is a powerful tool for processing highly repetitive
strings. We propose a new algorithm for online RLBWT working in run-compressed
space, which runs in time and bits of space, where
is the length of input string received so far and is the number of runs
in the BWT of the reversed . We improve the state-of-the-art algorithm for
online RLBWT in terms of empirical construction time. Adopting the dynamic list
for maintaining a total order, we can replace rank queries in a dynamic wavelet
tree on a run-length compressed string by the direct comparison of labels in a
dynamic list. The empirical result for various benchmarks show the efficiency
of our algorithm, especially for highly repetitive strings.Comment: In Proc. IWOCA201
The Wavelet Trie: Maintaining an Indexed Sequence of Strings in Compressed Space
An indexed sequence of strings is a data structure for storing a string
sequence that supports random access, searching, range counting and analytics
operations, both for exact matches and prefix search. String sequences lie at
the core of column-oriented databases, log processing, and other storage and
query tasks. In these applications each string can appear several times and the
order of the strings in the sequence is relevant. The prefix structure of the
strings is relevant as well: common prefixes are sought in strings to extract
interesting features from the sequence. Moreover, space-efficiency is highly
desirable as it translates directly into higher performance, since more data
can fit in fast memory.
We introduce and study the problem of compressed indexed sequence of strings,
representing indexed sequences of strings in nearly-optimal compressed space,
both in the static and dynamic settings, while preserving provably good
performance for the supported operations.
We present a new data structure for this problem, the Wavelet Trie, which
combines the classical Patricia Trie with the Wavelet Tree, a succinct data
structure for storing a compressed sequence. The resulting Wavelet Trie
smoothly adapts to a sequence of strings that changes over time. It improves on
the state-of-the-art compressed data structures by supporting a dynamic
alphabet (i.e. the set of distinct strings) and prefix queries, both crucial
requirements in the aforementioned applications, and on traditional indexes by
reducing space occupancy to close to the entropy of the sequence
Online Pattern Matching for String Edit Distance with Moves
Edit distance with moves (EDM) is a string-to-string distance measure that
includes substring moves in addition to ordinal editing operations to turn one
string to the other. Although optimizing EDM is intractable, it has many
applications especially in error detections. Edit sensitive parsing (ESP) is an
efficient parsing algorithm that guarantees an upper bound of parsing
discrepancies between different appearances of the same substrings in a string.
ESP can be used for computing an approximate EDM as the L1 distance between
characteristic vectors built by node labels in parsing trees. However, ESP is
not applicable to a streaming text data where a whole text is unknown in
advance. We present an online ESP (OESP) that enables an online pattern
matching for EDM. OESP builds a parse tree for a streaming text and computes
the L1 distance between characteristic vectors in an online manner. For the
space-efficient computation of EDM, OESP directly encodes the parse tree into a
succinct representation by leveraging the idea behind recent results of a
dynamic succinct tree. We experimentally test OESP on the ability to compute
EDM in an online manner on benchmark datasets, and we show OESP's efficiency.Comment: This paper has been accepted to the 21st edition of the International
Symposium on String Processing and Information Retrieval (SPIRE2014
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