New Algorithms and Lower Bounds for Sequential-Access Data Compression

TL;DR

This thesis introduces new algorithms and bounds for sequential-access data compression, including adaptive prefix coding, memory-constrained compression, and stream-based universal compression, highlighting the tradeoffs and minimal stream requirements.

Contribution

It presents novel algorithms for adaptive prefix coding with constant-time operations, characterizes memory-compression tradeoffs, and establishes the minimal number of streams needed for certain universal compression bounds.

Findings

Constant-time encoding and decoding for adaptive prefix coding.

Nearly tight tradeoff between memory and compression quality.

Two streams are necessary and sufficient for entropy-only bounds.

Abstract

This thesis concerns sequential-access data compression, i.e., by algorithms that read the input one or more times from beginning to end. In one chapter we consider adaptive prefix coding, for which we must read the input character by character, outputting each character's self-delimiting codeword before reading the next one. We show how to encode and decode each character in constant worst-case time while producing an encoding whose length is worst-case optimal. In another chapter we consider one-pass compression with memory bounded in terms of the alphabet size and context length, and prove a nearly tight tradeoff between the amount of memory we can use and the quality of the compression we can achieve. In a third chapter we consider compression in the read/write streams model, which allows us passes and memory both polylogarithmic in the size of the input. We first show how to achieve universal compression using only one pass over one stream. We then show that one stream is not sufficient for achieving good grammar-based compression. Finally, we show that two streams are necessary and sufficient for achieving entropy-only bounds.