7,553 research outputs found
Random Access to Grammar Compressed Strings
Grammar based compression, where one replaces a long string by a small
context-free grammar that generates the string, is a simple and powerful
paradigm that captures many popular compression schemes. In this paper, we
present a novel grammar representation that allows efficient random access to
any character or substring without decompressing the string.
Let be a string of length compressed into a context-free grammar
of size . We present two representations of
achieving random access time, and either
construction time and space on the pointer machine model, or
construction time and space on the RAM. Here, is the inverse of
the row of Ackermann's function. Our representations also efficiently
support decompression of any substring in : we can decompress any substring
of length in the same complexity as a single random access query and
additional time. Combining these results with fast algorithms for
uncompressed approximate string matching leads to several efficient algorithms
for approximate string matching on grammar-compressed strings without
decompression. For instance, we can find all approximate occurrences of a
pattern with at most errors in time , where is the number of occurrences of in . Finally, we
generalize our results to navigation and other operations on grammar-compressed
ordered trees.
All of the above bounds significantly improve the currently best known
results. To achieve these bounds, we introduce several new techniques and data
structures of independent interest, including a predecessor data structure, two
"biased" weighted ancestor data structures, and a compact representation of
heavy paths in grammars.Comment: Preliminary version in SODA 201
Faster subsequence recognition in compressed strings
Computation on compressed strings is one of the key approaches to processing
massive data sets. We consider local subsequence recognition problems on
strings compressed by straight-line programs (SLP), which is closely related to
Lempel--Ziv compression. For an SLP-compressed text of length , and an
uncompressed pattern of length , C{\'e}gielski et al. gave an algorithm for
local subsequence recognition running in time . We improve
the running time to . Our algorithm can also be used to
compute the longest common subsequence between a compressed text and an
uncompressed pattern in time ; the same problem with a
compressed pattern is known to be NP-hard
Improved Approximate String Matching and Regular Expression Matching on Ziv-Lempel Compressed Texts
We study the approximate string matching and regular expression matching
problem for the case when the text to be searched is compressed with the
Ziv-Lempel adaptive dictionary compression schemes. We present a time-space
trade-off that leads to algorithms improving the previously known complexities
for both problems. In particular, we significantly improve the space bounds,
which in practical applications are likely to be a bottleneck
A practical index for approximate dictionary matching with few mismatches
Approximate dictionary matching is a classic string matching problem
(checking if a query string occurs in a collection of strings) with
applications in, e.g., spellchecking, online catalogs, geolocation, and web
searchers. We present a surprisingly simple solution called a split index,
which is based on the Dirichlet principle, for matching a keyword with few
mismatches, and experimentally show that it offers competitive space-time
tradeoffs. Our implementation in the C++ language is focused mostly on data
compaction, which is beneficial for the search speed (e.g., by being cache
friendly). We compare our solution with other algorithms and we show that it
performs better for the Hamming distance. Query times in the order of 1
microsecond were reported for one mismatch for the dictionary size of a few
megabytes on a medium-end PC. We also demonstrate that a basic compression
technique consisting in -gram substitution can significantly reduce the
index size (up to 50% of the input text size for the DNA), while still keeping
the query time relatively low
Prospects and limitations of full-text index structures in genome analysis
The combination of incessant advances in sequencing technology producing large amounts of data and innovative bioinformatics approaches, designed to cope with this data flood, has led to new interesting results in the life sciences. Given the magnitude of sequence data to be processed, many bioinformatics tools rely on efficient solutions to a variety of complex string problems. These solutions include fast heuristic algorithms and advanced data structures, generally referred to as index structures. Although the importance of index structures is generally known to the bioinformatics community, the design and potency of these data structures, as well as their properties and limitations, are less understood. Moreover, the last decade has seen a boom in the number of variant index structures featuring complex and diverse memory-time trade-offs. This article brings a comprehensive state-of-the-art overview of the most popular index structures and their recently developed variants. Their features, interrelationships, the trade-offs they impose, but also their practical limitations, are explained and compared
- …