  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.
