Related papers: PivotCompress: Compression by Sorting
The goal of this thesis is to study the compression problems arising in distributed computing systematically. In the first part of the thesis, we study gradient compression for distributed first-order optimization. We begin by establishing…
Sorting database tables before compressing them improves the compression rate. Can we do better than the lexicographical order? For minimizing the number of runs in a run-length encoding compression scheme, the best approaches to…
Huffman encoding is often improved by using block codes, for example a 3-block would be an alphabet consisting of each possible combination of three characters. We take the approach of starting with a base alphabet and expanding it to…
Bitmap indexes must be compressed to reduce input/output costs and minimize CPU usage. To accelerate logical operations (AND, OR, XOR) over bitmaps, we use techniques based on run-length encoding (RLE), such as Word-Aligned Hybrid (WAH)…
Compression also known as entropy coding has a rich and long history. However, a recent explosion of multimedia Internet applications (such as teleconferencing and video streaming for instance) renews an interest in fast compression that…
Sorting a set of items is a task that can be useful by itself or as a building block for more complex operations. That is why a lot of effort has been put into finding sorting algorithms that sort large sets as fast as possible. But the…
Variable-length compression without prefix-free constraints and with side-information available at both encoder and decoder is considered. Instead of requiring the code to be error-free, we allow for it to have a non-vanishing error…
Sample compression schemes were defined by Littlestone and Warmuth (1986) as an abstraction of the structure underlying many learning algorithms. In a sample compression scheme, we are given a large sample of vertices of a fixed hypergraph…
A new data-enabled control technique for uncertain linear time-invariant systems, recently conceived by Coulson et\ al., builds upon the direct optimization of controllers over input/output pairs drawn from a large dataset. We adopt an…
Universal compression of patterns of sequences generated by independently identically distributed (i.i.d.) sources with unknown, possibly large, alphabets is investigated. A pattern is a sequence of indices that contains all consecutive…
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…
In this paper will be presented new approach to entropy coding: family of generalizations of standard numeral systems which are optimal for encoding sequence of equiprobable symbols, into asymmetric numeral systems - optimal for freely…
The goal of lossy data compression is to reduce the storage cost of a data set $X$ while retaining as much information as possible about something ($Y$) that you care about. For example, what aspects of an image $X$ contain the most…
Compressed sensing is a signal processing technique that allows for the reconstruction of a signal from a small set of measurements. The key idea behind compressed sensing is that many real-world signals are inherently sparse, meaning that…
Distributed systems, such as biological and artificial neural networks, process information via complex interactions engaging multiple subsystems, resulting in high-order patterns with distinct properties across scales. Investigating how…
Lossy image compression is generally formulated as a joint rate-distortion optimization to learn encoder, quantizer, and decoder. However, the quantizer is non-differentiable, and discrete entropy estimation usually is required for rate…
The weak law of large numbers implies that, under mild assumptions on the source, the Renyi entropy per produced symbol converges (in probability) towards the Shannon entropy rate. This paper quantifies the speed of this convergence for…
In image compression, with recent advances in generative modeling, the existence of a trade-off between the rate and the perceptual quality (realism) has been brought to light, where the realism is measured by the closeness of the output…
Many scientific codes and instruments generate large amounts of floating-point data at high rates that must be compressed before they can be stored. Typically, only lossy compression algorithms deliver high-enough compression ratios.…
We revisit the well-known problem of sorting under partial information: sort a finite set given the outcomes of comparisons between some pairs of elements. The input is a partially ordered set P, and solving the problem amounts to…