1,660 research outputs found
Compressed Indexes for String Searching in Labeled Graphs
Storing and searching large labeled graphs is indeed becoming a key issue in the design of space/time efficient online platforms indexing modern social networks or knowledge graphs. But, as far as we know, all these results are limited to design compressed graph indexes which support basic access operations onto the link structure of the input graph, such as: given a node u, return the adjacency list of u. This paper takes inspiration from the Facebook Unicorn's platform and proposes some compressed-indexing schemes for large graphs whose nodes are labeled with strings of variable length - i.e., node's attributes such as user's (nick-)name - that support sophisticated search operations which involve both the linked structure of the graph and the string content of its nodes.
An extensive experimental evaluation over real social networks will show the time and space efficiency of the proposed indexing schemes and their query processing algorithms
Compact Binary Relation Representations with Rich Functionality
Binary relations are an important abstraction arising in many data
representation problems. The data structures proposed so far to represent them
support just a few basic operations required to fit one particular application.
We identify many of those operations arising in applications and generalize
them into a wide set of desirable queries for a binary relation representation.
We also identify reductions among those operations. We then introduce several
novel binary relation representations, some simple and some quite
sophisticated, that not only are space-efficient but also efficiently support a
large subset of the desired queries.Comment: 32 page
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
Compressed Text Indexes:From Theory to Practice!
A compressed full-text self-index represents a text in a compressed form and
still answers queries efficiently. This technology represents a breakthrough
over the text indexing techniques of the previous decade, whose indexes
required several times the size of the text. Although it is relatively new,
this technology has matured up to a point where theoretical research is giving
way to practical developments. Nonetheless this requires significant
programming skills, a deep engineering effort, and a strong algorithmic
background to dig into the research results. To date only isolated
implementations and focused comparisons of compressed indexes have been
reported, and they missed a common API, which prevented their re-use or
deployment within other applications.
The goal of this paper is to fill this gap. First, we present the existing
implementations of compressed indexes from a practitioner's point of view.
Second, we introduce the Pizza&Chili site, which offers tuned implementations
and a standardized API for the most successful compressed full-text
self-indexes, together with effective testbeds and scripts for their automatic
validation and test. Third, we show the results of our extensive experiments on
these codes with the aim of demonstrating the practical relevance of this novel
and exciting technology
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
Composite repetition-aware data structures
In highly repetitive strings, like collections of genomes from the same
species, distinct measures of repetition all grow sublinearly in the length of
the text, and indexes targeted to such strings typically depend only on one of
these measures. We describe two data structures whose size depends on multiple
measures of repetition at once, and that provide competitive tradeoffs between
the time for counting and reporting all the exact occurrences of a pattern, and
the space taken by the structure. The key component of our constructions is the
run-length encoded BWT (RLBWT), which takes space proportional to the number of
BWT runs: rather than augmenting RLBWT with suffix array samples, we combine it
with data structures from LZ77 indexes, which take space proportional to the
number of LZ77 factors, and with the compact directed acyclic word graph
(CDAWG), which takes space proportional to the number of extensions of maximal
repeats. The combination of CDAWG and RLBWT enables also a new representation
of the suffix tree, whose size depends again on the number of extensions of
maximal repeats, and that is powerful enough to support matching statistics and
constant-space traversal.Comment: (the name of the third co-author was inadvertently omitted from
previous version
Subpath Queries on Compressed Graphs: A Survey
Text indexing is a classical algorithmic problem that has been studied for over four decades: given a text T, pre-process it off-line so that, later, we can quickly count and locate the occurrences of any string (the query pattern) in T in time proportional to the query’s length. The earliest optimal-time solution to the problem, the suffix tree, dates back to 1973 and requires up to two orders of magnitude more space than the plain text just to be stored. In the year 2000, two breakthrough works showed that efficient queries can be achieved without this space overhead: a fast index be stored in a space proportional to the text’s entropy. These contributions had an enormous impact in bioinformatics: today, virtually any DNA aligner employs compressed indexes. Recent trends considered more powerful compression schemes (dictionary compressors) and generalizations of the problem to labeled graphs: after all, texts can be viewed as labeled directed paths. In turn, since finite state automata can be considered as a particular case of labeled graphs, these findings created a bridge between the fields of compressed indexing and regular language theory, ultimately allowing to index regular languages and promising to shed new light on problems, such as regular expression matching. This survey is a gentle introduction to the main landmarks of the fascinating journey that took us from suffix trees to today’s compressed indexes for labeled graphs and regular languages
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