On Optimally Partitioning Variable-Byte Codes

The ubiquitous Variable-Byte encoding is one of the fastest compressed representation for integer sequences. However, its compression ratio is usually not competitive with other more sophisticated encoders, especially when the integers to be compressed are small that is the typical case for inverted indexes. This paper shows that the compression ratio of Variable-Byte can be improved by 2x by adopting a partitioned representation of the inverted lists. This makes Variable-Byte surprisingly competitive in space with the best bit-aligned encoders, hence disproving the folklore belief that Variable-Byte is space-inefficient for inverted index compression. Despite the significant space savings, we show that our optimization almost comes for free, given that: we introduce an optimal partitioning algorithm that does not affect indexing time because of its linear-time complexity; we show that the query processing speed of Variable-Byte is preserved, with an extensive experimental analysis and comparison with several other state-of-the-art encoders.Comment: Published in IEEE Transactions on Knowledge and Data Engineering (TKDE), 15 April 201

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

Cross-Sender Bit-Mixing Coding

Scheduling to avoid packet collisions is a long-standing challenge in networking, and has become even trickier in wireless networks with multiple senders and multiple receivers. In fact, researchers have proved that even {\em perfect} scheduling can only achieve $\mathbf{R} = O(\frac{1}{\ln N})$. Here $N$ is the number of nodes in the network, and $\mathbf{R}$ is the {\em medium utilization rate}. Ideally, one would hope to achieve $\mathbf{R} = \Theta(1)$, while avoiding all the complexities in scheduling. To this end, this paper proposes {\em cross-sender bit-mixing coding} ({\em BMC}), which does not rely on scheduling. Instead, users transmit simultaneously on suitably-chosen slots, and the amount of overlap in different user's slots is controlled via coding. We prove that in all possible network topologies, using BMC enables us to achieve $\mathbf{R}=\Theta(1)$. We also prove that the space and time complexities of BMC encoding/decoding are all low-order polynomials.Comment: Published in the International Conference on Information Processing in Sensor Networks (IPSN), 201

Re-Pair Compression of Inverted Lists

Compression of inverted lists with methods that support fast intersection operations is an active research topic. Most compression schemes rely on encoding differences between consecutive positions with techniques that favor small numbers. In this paper we explore a completely different alternative: We use Re-Pair compression of those differences. While Re-Pair by itself offers fast decompression at arbitrary positions in main and secondary memory, we introduce variants that in addition speed up the operations required for inverted list intersection. We compare the resulting data structures with several recent proposals under various list intersection algorithms, to conclude that our Re-Pair variants offer an interesting time/space tradeoff for this problem, yet further improvements are required for it to improve upon the state of the art