22,408 research outputs found
Indexing labeled sequences
International audienceBackground: Labels are a way to add some information on a text, such as functional annotations such as genes on a DNA sequences. V(D)J recombinations are DNA recombinations involving two or three short genes in lymphocytes. Sequencing this short region (500 bp or less) produces labeled sequences and brings insight in the lymphocyte repertoire for onco-hematology or immunology studies. Methods: We present two indexes for a text with non-overlapping labels. They store the text in a Burrows–Wheeler transform (BWT) and a compressed label sequence in a Wavelet Tree. The label sequence is taken in the order of the text (TL-index) or in the order of the BWT (TL-BW-index). Both indexes need a space related to the entropy of the labeled text. Results: These indexes allow efficient text–label queries to count and find labeled patterns. The TL-BW-index has an overhead on simple label queries but is very efficient on combined pattern–label queries. We implemented the indexes in C++ and compared them against a baseline solution on pseudo-random as well as on V(D)J labeled texts. Discussion: New indexes such as the ones we proposed improve the way we index and query labeled texts as, for instance, lymphocyte repertoire for hematological and immunological studies
Regular Languages meet Prefix Sorting
Indexing strings via prefix (or suffix) sorting is, arguably, one of the most
successful algorithmic techniques developed in the last decades. Can indexing
be extended to languages? The main contribution of this paper is to initiate
the study of the sub-class of regular languages accepted by an automaton whose
states can be prefix-sorted. Starting from the recent notion of Wheeler graph
[Gagie et al., TCS 2017]-which extends naturally the concept of prefix sorting
to labeled graphs-we investigate the properties of Wheeler languages, that is,
regular languages admitting an accepting Wheeler finite automaton.
Interestingly, we characterize this family as the natural extension of regular
languages endowed with the co-lexicographic ordering: when sorted, the strings
belonging to a Wheeler language are partitioned into a finite number of
co-lexicographic intervals, each formed by elements from a single Myhill-Nerode
equivalence class. Moreover: (i) We show that every Wheeler NFA (WNFA) with
states admits an equivalent Wheeler DFA (WDFA) with at most
states that can be computed in time. This is in sharp contrast with
general NFAs. (ii) We describe a quadratic algorithm to prefix-sort a proper
superset of the WDFAs, a -time online algorithm to sort acyclic
WDFAs, and an optimal linear-time offline algorithm to sort general WDFAs. By
contribution (i), our algorithms can also be used to index any WNFA at the
moderate price of doubling the automaton's size. (iii) We provide a
minimization theorem that characterizes the smallest WDFA recognizing the same
language of any input WDFA. The corresponding constructive algorithm runs in
optimal linear time in the acyclic case, and in time in the
general case. (iv) We show how to compute the smallest WDFA equivalent to any
acyclic DFA in nearly-optimal time.Comment: added minimization theorems; uploaded submitted version; New version
with new results (W-MH theorem, linear determinization), added author:
Giovanna D'Agostin
LR characterization of chirotopes of finite planar families of pairwise disjoint convex bodies
We extend the classical LR characterization of chirotopes of finite planar
families of points to chirotopes of finite planar families of pairwise disjoint
convex bodies: a map \c{hi} on the set of 3-subsets of a finite set I is a
chirotope of finite planar families of pairwise disjoint convex bodies if and
only if for every 3-, 4-, and 5-subset J of I the restriction of \c{hi} to the
set of 3-subsets of J is a chirotope of finite planar families of pairwise
disjoint convex bodies. Our main tool is the polarity map, i.e., the map that
assigns to a convex body the set of lines missing its interior, from which we
derive the key notion of arrangements of double pseudolines, introduced for the
first time in this paper.Comment: 100 pages, 73 figures; accepted manuscript versio
Suffix Tree of Alignment: An Efficient Index for Similar Data
We consider an index data structure for similar strings. The generalized
suffix tree can be a solution for this. The generalized suffix tree of two
strings and is a compacted trie representing all suffixes in and
. It has leaves and can be constructed in time.
However, if the two strings are similar, the generalized suffix tree is not
efficient because it does not exploit the similarity which is usually
represented as an alignment of and .
In this paper we propose a space/time-efficient suffix tree of alignment
which wisely exploits the similarity in an alignment. Our suffix tree for an
alignment of and has leaves where is the sum of
the lengths of all parts of different from and is the sum of the
lengths of some common parts of and . We did not compromise the pattern
search to reduce the space. Our suffix tree can be searched for a pattern
in time where is the number of occurrences of in and
. We also present an efficient algorithm to construct the suffix tree of
alignment. When the suffix tree is constructed from scratch, the algorithm
requires time where is the sum of the lengths
of other common substrings of and . When the suffix tree of is
already given, it requires time.Comment: 12 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
CiNCT: Compression and retrieval for massive vehicular trajectories via relative movement labeling
In this paper, we present a compressed data structure for moving object
trajectories in a road network, which are represented as sequences of road
edges. Unlike existing compression methods for trajectories in a network, our
method supports pattern matching and decompression from an arbitrary position
while retaining a high compressibility with theoretical guarantees.
Specifically, our method is based on FM-index, a fast and compact data
structure for pattern matching. To enhance the compression, we incorporate the
sparsity of road networks into the data structure. In particular, we present
the novel concepts of relative movement labeling and PseudoRank, each
contributing to significant reductions in data size and query processing time.
Our theoretical analysis and experimental studies reveal the advantages of our
proposed method as compared to existing trajectory compression methods and
FM-index variants
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