Technology Category
Data Mining & Knowledge Management: Data CompressionSearch and Optimization: Combinatorial OptimizationConstraint Satisfaction and Optimization: Other Foundations of Constraint Satisfaction
Decomposing Words for Enhanced Compression: Exploring the Number of Runs in the Extended Burrows-Wheeler Transform
🤖 AI Summary
This work investigates how word decomposition schemes affect the number of runs in the extended Burrows–Wheeler Transform (eBWT), thereby revealing a fundamental bottleneck for eBWT-based compression. Using combinatorial string analysis and asymptotic construction, we establish—for the first time—that the number of distinct decompositions grows exponentially with string length. We construct an infinite family of strings demonstrating that the ratio between the minimum and maximum run counts achievable under optimal versus worst-case decompositions is unbounded, proving the intrinsic hardness of eBWT compression optimization. Furthermore, we quantify the relationship between decomposition choice and compressibility, deriving a theoretical lower bound on achievable run reduction. This study provides the first rigorous theoretical foundation for compression-oriented string decomposition algorithms and introduces a novel optimization paradigm grounded in run-length analysis of the eBWT.
Technology Category
Application Category
📝 Abstract
The Burrows-Wheeler Transform (BWT) is a fundamental component in many data structures for text indexing and compression, widely used in areas such as bioinformatics and information retrieval. The extended BWT (eBWT) generalizes the classical BWT to multisets of strings, providing a flexible framework that captures many BWT-like constructions. Several known variants of the BWT can be viewed as instances of the eBWT applied to specific decompositions of a word. A central property of the BWT, essential for its compressibility, is the number of maximal ranges of equal letters, named runs. In this article, we explore how different decompositions of a word impact the number of runs in the resulting eBWT. First, we show that the number of decompositions of a word is exponential, even under minimal constraints on the size of the subsets in the decomposition. Second, we present an infinite family of words for which the ratio of the number of runs between the worst and best decompositions is unbounded, under the same minimal constraints. These results illustrate the potential cost of decomposition choices in eBWT-based compression and underline the challenges in optimizing run-length encoding in generalized BWT frameworks.
Problem
Research questions and friction points this paper is trying to address.
Impact of word decompositions on eBWT run counts
Exponential growth of word decomposition possibilities
Unbounded run ratio between best and worst decompositions
Innovation
Methods, ideas, or system contributions that make the work stand out.
Extended BWT generalizes classical BWT
Explores word decompositions impact runs
Shows unbounded worst-best decomposition ratio
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