On optimally partitioning a text to improve its compression

In this paper we investigate the problem of partitioning an input string T in such a way that compressing individually its parts via a base-compressor C gets a compressed output that is shorter than applying C over the entire T at once. This problem was introduced in the context of table compression, and then further elaborated and extended to strings and trees. Unfortunately, the literature offers poor solutions: namely, we know either a cubic-time algorithm for computing the optimal partition based on dynamic programming, or few heuristics that do not guarantee any bounds on the efficacy of their computed partition, or algorithms that are efficient but work in some specific scenarios (such as the Burrows-Wheeler Transform) and achieve compression performance that might be worse than the optimal-partitioning by a $\Omega(\sqrt{\log n})$ factor. Therefore, computing efficiently the optimal solution is still open. In this paper we provide the first algorithm which is guaranteed to compute in O(n \log_{1+\eps}n) time a partition of T whose compressed output is guaranteed to be no more than $(1+\epsilon)$-worse the optimal one, where $\epsilon$ may be any positive constant

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

Navigation domain representation for interactive multiview imaging

Enabling users to interactively navigate through different viewpoints of a static scene is a new interesting functionality in 3D streaming systems. While it opens exciting perspectives towards rich multimedia applications, it requires the design of novel representations and coding techniques in order to solve the new challenges imposed by interactive navigation. Interactivity clearly brings new design constraints: the encoder is unaware of the exact decoding process, while the decoder has to reconstruct information from incomplete subsets of data since the server can generally not transmit images for all possible viewpoints due to resource constrains. In this paper, we propose a novel multiview data representation that permits to satisfy bandwidth and storage constraints in an interactive multiview streaming system. In particular, we partition the multiview navigation domain into segments, each of which is described by a reference image and some auxiliary information. The auxiliary information enables the client to recreate any viewpoint in the navigation segment via view synthesis. The decoder is then able to navigate freely in the segment without further data request to the server; it requests additional data only when it moves to a different segment. We discuss the benefits of this novel representation in interactive navigation systems and further propose a method to optimize the partitioning of the navigation domain into independent segments, under bandwidth and storage constraints. Experimental results confirm the potential of the proposed representation; namely, our system leads to similar compression performance as classical inter-view coding, while it provides the high level of flexibility that is required for interactive streaming. Hence, our new framework represents a promising solution for 3D data representation in novel interactive multimedia services

Weighted universal image compression

We describe a general coding strategy leading to a family of universal image compression systems designed to give good performance in applications where the statistics of the source to be compressed are not available at design time or vary over time or space. The basic approach considered uses a two-stage structure in which the single source code of traditional image compression systems is replaced with a family of codes designed to cover a large class of possible sources. To illustrate this approach, we consider the optimal design and use of two-stage codes containing collections of vector quantizers (weighted universal vector quantization), bit allocations for JPEG-style coding (weighted universal bit allocation), and transform codes (weighted universal transform coding). Further, we demonstrate the benefits to be gained from the inclusion of perceptual distortion measures and optimal parsing. The strategy yields two-stage codes that significantly outperform their single-stage predecessors. On a sequence of medical images, weighted universal vector quantization outperforms entropy coded vector quantization by over 9 dB. On the same data sequence, weighted universal bit allocation outperforms a JPEG-style code by over 2.5 dB. On a collection of mixed test and image data, weighted universal transform coding outperforms a single, data-optimized transform code (which gives performance almost identical to that of JPEG) by over 6 dB

On the List Update Problem with Advice

We study the online list update problem under the advice model of computation. Under this model, an online algorithm receives partial information about the unknown parts of the input in the form of some bits of advice generated by a benevolent offline oracle. We show that advice of linear size is required and sufficient for a deterministic algorithm to achieve an optimal solution or even a competitive ratio better than $15/14$. On the other hand, we show that surprisingly two bits of advice are sufficient to break the lower bound of $2$ on the competitive ratio of deterministic online algorithms and achieve a deterministic algorithm with a competitive ratio of $5/3$. In this upper-bound argument, the bits of advice determine the algorithm with smaller cost among three classical online algorithms, TIMESTAMP and two members of the MTF2 family of algorithms. We also show that MTF2 algorithms are $2.5$-competitive

Compressed Representations of Permutations, and Applications

We explore various techniques to compress a permutation $\pi$ over n integers, taking advantage of ordered subsequences in $\pi$, while supporting its application $\pi$(i) and the application of its inverse $\pi^{-1}(i)$ in small time. Our compression schemes yield several interesting byproducts, in many cases matching, improving or extending the best existing results on applications such as the encoding of a permutation in order to support iterated applications $\pi^k(i)$ of it, of integer functions, and of inverted lists and suffix arrays

LRM-Trees: Compressed Indices, Adaptive Sorting, and Compressed Permutations

LRM-Trees are an elegant way to partition a sequence of values into sorted consecutive blocks, and to express the relative position of the first element of each block within a previous block. They were used to encode ordinal trees and to index integer arrays in order to support range minimum queries on them. We describe how they yield many other convenient results in a variety of areas, from data structures to algorithms: some compressed succinct indices for range minimum queries; a new adaptive sorting algorithm; and a compressed succinct data structure for permutations supporting direct and indirect application in time all the shortest as the permutation is compressible.Comment: 13 pages, 1 figur