5,930 research outputs found
Weighted ancestors in suffix trees
The classical, ubiquitous, predecessor problem is to construct a data
structure for a set of integers that supports fast predecessor queries. Its
generalization to weighted trees, a.k.a. the weighted ancestor problem, has
been extensively explored and successfully reduced to the predecessor problem.
It is known that any solution for both problems with an input set from a
polynomially bounded universe that preprocesses a weighted tree in O(n
polylog(n)) space requires \Omega(loglogn) query time. Perhaps the most
important and frequent application of the weighted ancestors problem is for
suffix trees. It has been a long-standing open question whether the weighted
ancestors problem has better bounds for suffix trees. We answer this question
positively: we show that a suffix tree built for a text w[1..n] can be
preprocessed using O(n) extra space, so that queries can be answered in O(1)
time. Thus we improve the running times of several applications. Our
improvement is based on a number of data structure tools and a
periodicity-based insight into the combinatorial structure of a suffix tree.Comment: 27 pages, LNCS format. A condensed version will appear in ESA 201
Fast, Small and Exact: Infinite-order Language Modelling with Compressed Suffix Trees
Efficient methods for storing and querying are critical for scaling
high-order n-gram language models to large corpora. We propose a language model
based on compressed suffix trees, a representation that is highly compact and
can be easily held in memory, while supporting queries needed in computing
language model probabilities on-the-fly. We present several optimisations which
improve query runtimes up to 2500x, despite only incurring a modest increase in
construction time and memory usage. For large corpora and high Markov orders,
our method is highly competitive with the state-of-the-art KenLM package. It
imposes much lower memory requirements, often by orders of magnitude, and has
runtimes that are either similar (for training) or comparable (for querying).Comment: 14 pages in Transactions of the Association for Computational
Linguistics (TACL) 201
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
Handling Massive N-Gram Datasets Efficiently
This paper deals with the two fundamental problems concerning the handling of
large n-gram language models: indexing, that is compressing the n-gram strings
and associated satellite data without compromising their retrieval speed; and
estimation, that is computing the probability distribution of the strings from
a large textual source. Regarding the problem of indexing, we describe
compressed, exact and lossless data structures that achieve, at the same time,
high space reductions and no time degradation with respect to state-of-the-art
solutions and related software packages. In particular, we present a compressed
trie data structure in which each word following a context of fixed length k,
i.e., its preceding k words, is encoded as an integer whose value is
proportional to the number of words that follow such context. Since the number
of words following a given context is typically very small in natural
languages, we lower the space of representation to compression levels that were
never achieved before. Despite the significant savings in space, our technique
introduces a negligible penalty at query time. Regarding the problem of
estimation, we present a novel algorithm for estimating modified Kneser-Ney
language models, that have emerged as the de-facto choice for language modeling
in both academia and industry, thanks to their relatively low perplexity
performance. Estimating such models from large textual sources poses the
challenge of devising algorithms that make a parsimonious use of the disk. The
state-of-the-art algorithm uses three sorting steps in external memory: we show
an improved construction that requires only one sorting step thanks to
exploiting the properties of the extracted n-gram strings. With an extensive
experimental analysis performed on billions of n-grams, we show an average
improvement of 4.5X on the total running time of the state-of-the-art approach.Comment: Published in ACM Transactions on Information Systems (TOIS), February
2019, Article No: 2
Internal Pattern Matching Queries in a Text and Applications
We consider several types of internal queries: questions about subwords of a
text. As the main tool we develop an optimal data structure for the problem
called here internal pattern matching. This data structure provides
constant-time answers to queries about occurrences of one subword in
another subword of a given text, assuming that ,
which allows for a constant-space representation of all occurrences. This
problem can be viewed as a natural extension of the well-studied pattern
matching problem. The data structure has linear size and admits a linear-time
construction algorithm.
Using the solution to the internal pattern matching problem, we obtain very
efficient data structures answering queries about: primitivity of subwords,
periods of subwords, general substring compression, and cyclic equivalence of
two subwords. All these results improve upon the best previously known
counterparts. The linear construction time of our data structure also allows to
improve the algorithm for finding -subrepetitions in a text (a more
general version of maximal repetitions, also called runs). For any fixed
we obtain the first linear-time algorithm, which matches the linear
time complexity of the algorithm computing runs. Our data structure has already
been used as a part of the efficient solutions for subword suffix rank &
selection, as well as substring compression using Burrows-Wheeler transform
composed with run-length encoding.Comment: 31 pages, 9 figures; accepted to SODA 201
On Multilingual Training of Neural Dependency Parsers
We show that a recently proposed neural dependency parser can be improved by
joint training on multiple languages from the same family. The parser is
implemented as a deep neural network whose only input is orthographic
representations of words. In order to successfully parse, the network has to
discover how linguistically relevant concepts can be inferred from word
spellings. We analyze the representations of characters and words that are
learned by the network to establish which properties of languages were
accounted for. In particular we show that the parser has approximately learned
to associate Latin characters with their Cyrillic counterparts and that it can
group Polish and Russian words that have a similar grammatical function.
Finally, we evaluate the parser on selected languages from the Universal
Dependencies dataset and show that it is competitive with other recently
proposed state-of-the art methods, while having a simple structure.Comment: preprint accepted into the TSD201
On the tradeoff between stability and fit
In computing, as in many aspects of life, changes incur cost. Many optimization problems are formulated as a one-time instance starting from scratch. However, a common case that arises is when we already have a set of prior assignments and must decide how to respond to a new set of constraints, given that each change from the current assignment comes at a price. That is, we would like to maximize the fitness or efficiency of our system, but we need to balance it with the changeout cost from the previous state.
We provide a precise formulation for this tradeoff and analyze the resulting stable extensions of some fundamental problems in measurement and analytics. Our main technical contribution is a stable extension of Probability Proportional to Size (PPS) weighted random sampling, with applications to monitoring and anomaly detection problems. We also provide a general framework that applies to top-k, minimum spanning tree, and assignment. In both cases, we are able to provide exact solutions and discuss efficient incremental algorithms that can find new solutions as the input changes
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