Polylog space compression, pushdown compression, and Lempel-Ziv are incomparable

TL;DR

This paper compares pushdown compressors, polylog space compressors, and Lempel-Ziv algorithms, showing that their performance measures are fundamentally incomparable in the context of XML document compression.

Contribution

It introduces a formal model of pushdown compressors and analyzes their performance relative to polylog space algorithms and Lempel-Ziv, revealing their incomparability.

Findings

Pushdown compressors and polylog space compressors are incomparable in performance.

Lempel-Ziv algorithm's performance cannot be directly compared to pushdown or polylog space compressors.

The study provides a formal framework for analyzing different compression models in XML contexts.

Abstract

The pressing need for efficient compression schemes for XML documents has recently been focused on stack computation, and in particular calls for a formulation of information-lossless stack or pushdown compressors that allows a formal analysis of their performance and a more ambitious use of the stack in XML compression, where so far it is mainly connected to parsing mechanisms. In this paper we introduce the model of pushdown compressor, based on pushdown transducers that compute a single injective function while keeping the widest generality regarding stack computation. We also consider online compression algorithms that use at most polylogarithmic space (plogon). These algorithms correspond to compressors in the data stream model. We compare the performance of these two families of compressors with each other and with the general purpose Lempel-Ziv algorithm. This comparison is made without any a priori assumption on the data's source and considering the asymptotic compression ratio for infinite sequences. We prove that in all cases they are incomparable.