Related papers: New Algorithms and Lower Bounds for Sequential-Acc…
Can we use machine learning to compress graph data? The absence of ordering in graphs poses a significant challenge to conventional compression algorithms, limiting their attainable gains as well as their ability to discover relevant…
Learning, prediction, and compression are intimately connected: a model that accurately predicts the next symbol in a sequence can be coupled with a source coder to compress that sequence near its information-theoretic limit. When tokenized…
Most of the world's digital data is currently encoded in a sequential form, and compression methods for sequences have been studied extensively. However, there are many types of non-sequential data for which good compression techniques are…
We introduce a new computational model for data streams: asymptotically exact streaming algorithms. These algorithms have an approximation ratio that tends to one as the length of the stream goes to infinity while the memory used by the…
Many streaming algorithms provide only a high-probability relative approximation. These two relaxations, of allowing approximation and randomization, seem necessary -- for many streaming problems, both relaxations must be employed…
We introduce a new notion of information complexity for multi-pass streaming problems and use it to resolve several important questions in data streams. In the coin problem, one sees a stream of $n$ i.i.d. uniform bits and one would like to…
A prescription to calculate the minimum number of bits needed for binary strip detector readout is presented. This permits a systematic analysis of the readout efficiency relative to this theoretical minimum number of bits. Different level…
Non-uniquely decodable codes can be defined as the codes that cannot be uniquely decoded without additional disambiguation information. These are mainly the class of non-prefix-free codes, where a codeword can be a prefix of other(s), and…
We consider the problem of successive-refinement coding for lossy compression of individual sequences, namely, compression in two stages, where in the first stage, a coarse description at a relatively low rate is sent from the encoder to…
The traditional methods for data compression are typically based on the symbol-level statistics, with the information source modeled as a long sequence of i.i.d. random variables or a stochastic process, thus establishing the fundamental…
With the explosion of the size of digital dataset, the limiting factor for decomposition algorithms is the \emph{number of passes} over the input, as the input is often stored out-of-core or even off-site. Moreover, we're only interested in…
In many emerging applications, data streams are monitored in a network environment. Due to limited communication bandwidth and other resource constraints, a critical and practical demand is to online compress data streams continuously with…
Constrained coding plays a key role in optimizing performance and mitigating errors in applications such as storage and communication, where specific constraints on codewords are required. While non-parametric constraints have been…
In this paper, we propose {\em distributed network compression via memory}. We consider two spatially separated sources with correlated unknown source parameters. We wish to study the universal compression of a sequence of length $n$ from…
Grammar compression is a general compression framework in which a string $T$ of length $N$ is represented as a context-free grammar of size $n$ whose language contains only $T$. In this paper, we focus on studying the limitations of…
Language prediction is constrained by informational entropy intrinsic to language, such that there exists a limit to how accurate any language model can become and equivalently a lower bound to language compression. The most efficient…
The random access problem for compressed strings is to build a data structure that efficiently supports accessing the character in position $i$ of a string given in compressed form. Given a grammar of size $n$ compressing a string of size…
We consider the problem of optimally compressing and caching data across a communication network. Given the data generated at edge nodes and a routing path, our goal is to determine the optimal data compression ratios and caching decisions…
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…
This article describes lossless compression algorithms for multisets of sequences, taking advantage of the multiset's unordered structure. Multisets are a generalisation of sets where members are allowed to occur multiple times. A multiset…