3,872 research outputs found
The universality of iterated hashing over variable-length strings
Iterated hash functions process strings recursively, one character at a time.
At each iteration, they compute a new hash value from the preceding hash value
and the next character. We prove that iterated hashing can be pairwise
independent, but never 3-wise independent. We show that it can be almost
universal over strings much longer than the number of hash values; we bound the
maximal string length given the collision probability
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
Regular and almost universal hashing: an efficient implementation
Random hashing can provide guarantees regarding the performance of data
structures such as hash tables---even in an adversarial setting. Many existing
families of hash functions are universal: given two data objects, the
probability that they have the same hash value is low given that we pick hash
functions at random. However, universality fails to ensure that all hash
functions are well behaved. We further require regularity: when picking data
objects at random they should have a low probability of having the same hash
value, for any fixed hash function. We present the efficient implementation of
a family of non-cryptographic hash functions (PM+) offering good running times,
good memory usage as well as distinguishing theoretical guarantees: almost
universality and component-wise regularity. On a variety of platforms, our
implementations are comparable to the state of the art in performance. On
recent Intel processors, PM+ achieves a speed of 4.7 bytes per cycle for 32-bit
outputs and 3.3 bytes per cycle for 64-bit outputs. We review vectorization
through SIMD instructions (e.g., AVX2) and optimizations for superscalar
execution.Comment: accepted for publication in Software: Practice and Experience in
September 201
Practical Evaluation of Lempel-Ziv-78 and Lempel-Ziv-Welch Tries
We present the first thorough practical study of the Lempel-Ziv-78 and the
Lempel-Ziv-Welch computation based on trie data structures. With a careful
selection of trie representations we can beat well-tuned popular trie data
structures like Judy, m-Bonsai or Cedar
Improved Approximate String Matching and Regular Expression Matching on Ziv-Lempel Compressed Texts
We study the approximate string matching and regular expression matching
problem for the case when the text to be searched is compressed with the
Ziv-Lempel adaptive dictionary compression schemes. We present a time-space
trade-off that leads to algorithms improving the previously known complexities
for both problems. In particular, we significantly improve the space bounds,
which in practical applications are likely to be a bottleneck
- …