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

siEDM: an efficient string index and search algorithm for edit distance with moves

Although several self-indexes for highly repetitive text collections exist, developing an index and search algorithm with editing operations remains a challenge. Edit distance with moves (EDM) is a string-to-string distance measure that includes substring moves in addition to ordinal editing operations to turn one string into another. Although the problem of computing EDM is intractable, it has a wide range of potential applications, especially in approximate string retrieval. Despite the importance of computing EDM, there has been no efficient method for indexing and searching large text collections based on the EDM measure. We propose the first algorithm, named string index for edit distance with moves (siEDM), for indexing and searching strings with EDM. The siEDM algorithm builds an index structure by leveraging the idea behind the edit sensitive parsing (ESP), an efficient algorithm enabling approximately computing EDM with guarantees of upper and lower bounds for the exact EDM. siEDM efficiently prunes the space for searching query strings by the proposed method, which enables fast query searches with the same guarantee as ESP. We experimentally tested the ability of siEDM to index and search strings on benchmark datasets, and we showed siEDM's efficiency.Comment: 23 page

A practical index for approximate dictionary matching with few mismatches

Approximate dictionary matching is a classic string matching problem (checking if a query string occurs in a collection of strings) with applications in, e.g., spellchecking, online catalogs, geolocation, and web searchers. We present a surprisingly simple solution called a split index, which is based on the Dirichlet principle, for matching a keyword with few mismatches, and experimentally show that it offers competitive space-time tradeoffs. Our implementation in the C++ language is focused mostly on data compaction, which is beneficial for the search speed (e.g., by being cache friendly). We compare our solution with other algorithms and we show that it performs better for the Hamming distance. Query times in the order of 1 microsecond were reported for one mismatch for the dictionary size of a few megabytes on a medium-end PC. We also demonstrate that a basic compression technique consisting in $q$-gram substitution can significantly reduce the index size (up to 50% of the input text size for the DNA), while still keeping the query time relatively low