657 research outputs found
Universal Indexes for Highly Repetitive Document Collections
Indexing highly repetitive collections has become a relevant problem with the
emergence of large repositories of versioned documents, among other
applications. These collections may reach huge sizes, but are formed mostly of
documents that are near-copies of others. Traditional techniques for indexing
these collections fail to properly exploit their regularities in order to
reduce space.
We introduce new techniques for compressing inverted indexes that exploit
this near-copy regularity. They are based on run-length, Lempel-Ziv, or grammar
compression of the differential inverted lists, instead of the usual practice
of gap-encoding them. We show that, in this highly repetitive setting, our
compression methods significantly reduce the space obtained with classical
techniques, at the price of moderate slowdowns. Moreover, our best methods are
universal, that is, they do not need to know the versioning structure of the
collection, nor that a clear versioning structure even exists.
We also introduce compressed self-indexes in the comparison. These are
designed for general strings (not only natural language texts) and represent
the text collection plus the index structure (not an inverted index) in
integrated form. We show that these techniques can compress much further, using
a small fraction of the space required by our new inverted indexes. Yet, they
are orders of magnitude slower.Comment: This research has received funding from the European Union's Horizon
2020 research and innovation programme under the Marie Sk{\l}odowska-Curie
Actions H2020-MSCA-RISE-2015 BIRDS GA No. 69094
Document Retrieval on Repetitive Collections
Document retrieval aims at finding the most important documents where a
pattern appears in a collection of strings. Traditional pattern-matching
techniques yield brute-force document retrieval solutions, which has motivated
the research on tailored indexes that offer near-optimal performance. However,
an experimental study establishing which alternatives are actually better than
brute force, and which perform best depending on the collection
characteristics, has not been carried out. In this paper we address this
shortcoming by exploring the relationship between the nature of the underlying
collection and the performance of current methods. Via extensive experiments we
show that established solutions are often beaten in practice by brute-force
alternatives. We also design new methods that offer superior time/space
trade-offs, particularly on repetitive collections.Comment: Accepted to ESA 2014. Implementation and experiments at
http://www.cs.helsinki.fi/group/suds/rlcsa
Optimal-Time Text Indexing 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 , the number of runs in their Burrows-Wheeler Transform
(BWT). One of the earliest indexes for repetitive collections, the Run-Length
FM-index, used space and was able to efficiently count the number of
occurrences of a pattern of length 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
. Since then, a number of other indexes with space bounded by other measures
of repetitiveness --- the number of phrases in the Lempel-Ziv parse, the size
of the smallest grammar generating the text, the size of the smallest automaton
recognizing the text factors --- have been proposed for efficiently locating,
but not directly counting, the occurrences of a pattern. In this paper we close
this long-standing problem, showing how to extend the Run-Length FM-index so
that it can locate the occurrences efficiently within space (in
loglogarithmic time each), and reaching optimal time within
space, on a RAM machine of bits. Within
space, our index can also count in optimal time .
Raising the space to , we support count and locate in
and time, which is optimal in the
packed setting and had not been obtained before in compressed space. We also
describe a structure using space that replaces the text and
extracts any text substring of length in almost-optimal time
. (...continues...
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)
Universal Compressed Text Indexing
The rise of repetitive datasets has lately generated a lot of interest in
compressed self-indexes based on dictionary compression, a rich and
heterogeneous family that exploits text repetitions in different ways. For each
such compression scheme, several different indexing solutions have been
proposed in the last two decades. To date, the fastest indexes for repetitive
texts are based on the run-length compressed Burrows-Wheeler transform and on
the Compact Directed Acyclic Word Graph. The most space-efficient indexes, on
the other hand, are based on the Lempel-Ziv parsing and on grammar compression.
Indexes for more universal schemes such as collage systems and macro schemes
have not yet been proposed. Very recently, Kempa and Prezza [STOC 2018] showed
that all dictionary compressors can be interpreted as approximation algorithms
for the smallest string attractor, that is, a set of text positions capturing
all distinct substrings. Starting from this observation, in this paper we
develop the first universal compressed self-index, that is, the first indexing
data structure based on string attractors, which can therefore be built on top
of any dictionary-compressed text representation. Let be the size of a
string attractor for a text of length . Our index takes
words of space and supports locating the
occurrences of any pattern of length in
time, for any constant . This is, in particular, the first index
for general macro schemes and collage systems. Our result shows that the
relation between indexing and compression is much deeper than what was
previously thought: the simple property standing at the core of all dictionary
compressors is sufficient to support fast indexed queries.Comment: Fixed with reviewer's comment
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