1,085 research outputs found
Speeding-up -gram mining on grammar-based compressed texts
We present an efficient algorithm for calculating -gram frequencies on
strings represented in compressed form, namely, as a straight line program
(SLP). Given an SLP of size that represents string , the
algorithm computes the occurrence frequencies of all -grams in , by
reducing the problem to the weighted -gram frequencies problem on a
trie-like structure of size , where
is a quantity that represents the amount of
redundancy that the SLP captures with respect to -grams. The reduced problem
can be solved in linear time. Since , the running time of our
algorithm is , improving our
previous algorithm when
Reverse-Safe Data Structures for Text Indexing
We introduce the notion of reverse-safe data structures. These are data structures that prevent the reconstruction of the data they encode (i.e., they cannot be easily reversed). A data structure D is called z-reverse-safe when there exist at least z datasets with the same set of answers as the ones stored by D. The main challenge is to ensure that D stores as many answers to useful queries as possible, is constructed efficiently, and has size close to the size of the original dataset it encodes. Given a text of length n and an integer z, we propose an algorithm which constructs a z-reverse-safe data structure that has size O(n) and answers pattern matching queries of length at most d optimally, where d is maximal for any such z-reverse-safe data structure. The construction algorithm takes O(n ω log d) time, where ω is the matrix multiplication exponent. We show that, despite the n ω factor, our engineered implementation takes only a few minutes to finish for million-letter texts. We further show that plugging our method in data analysis applications gives insignificant or no data utility loss. Finally, we show how our technique can be extended to support applications under a realistic adversary model
Data Structures for Efficient String Algorithms
This thesis deals with data structures that are mostly useful in the area of string matching and string mining. Our main result is an O(n)-time preprocessing scheme for an array of n numbers such that subsequent queries asking for the position of a minimum element in a specified interval can be answered in constant time (so-called RMQs for Range Minimum Queries). The space for this data structure is 2n+o(n) bits, which is shown to be asymptotically optimal in a general setting. This improves all previous results on this problem. The main techniques for deriving this result rely on combinatorial properties of arrays and so-called Cartesian Trees. For compressible input arrays we show that further space can be saved, while not affecting the time bounds. For the two-dimensional variant of the RMQ-problem we give a preprocessing scheme with quasi-optimal time bounds, but with an asymptotic increase in space consumption of a factor of log(n).
It is well known that algorithms for answering RMQs in constant time are useful for many different algorithmic tasks (e.g., the computation of lowest common ancestors in trees); in the second part of this thesis we give several new applications of the RMQ-problem. We show that our preprocessing scheme for RMQ (and a variant thereof) leads to improvements in the space- and time-consumption of the Enhanced Suffix Array, a collection of arrays that can be used for many tasks in pattern matching. In particular, we will see that in conjunction with the suffix- and LCP-array 2n+o(n) bits of additional space (coming from our RMQ-scheme) are sufficient to find all occ occurrences of a (usually short) pattern of length m in a (usually long) text of length n in O(m*s+occ) time, where s denotes the size of the alphabet. This is certainly optimal if the size of the alphabet is constant; for non-constant alphabets we can improve this to O(m*log(s)+occ) locating time, replacing our original scheme with a data structure of size approximately 2.54n bits. Again by using RMQs, we then show how to solve frequency-related string mining tasks in optimal time. In a final chapter we propose a space- and time-optimal algorithm for computing suffix arrays on texts that are logically divided into words, if one is just interested in finding all word-aligned occurrences of a pattern.
Apart from the theoretical improvements made in this thesis, most of our algorithms are also of practical value; we underline this fact by empirical tests and comparisons on real-word problem instances. In most cases our algorithms outperform previous approaches by all means
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
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