Ladderpath: An Efficient Algorithm for Revealing Nested Hierarchy in Sequences

Ladderpath is a method rooted in the principles of Algorithmic Information Theory (AIT) for uncovering nested and hierarchical structures in symbolic sequences through minimal compositional reconstruction. It approximates Kolmogorov complexity by identifying reusable subsequences that enable efficient reconstruction of complex sequences. The proposed algorithm improves upon earlier implementations by introducing key optimizations in substring enumeration and reuse filtering, allowing it to scale to sequence systems with tens or even hundreds of millions of characters. Ladderpath produces a standardized JSON format that encodes compositional dependencies and hierarchies, and supports a variety of downstream tasks, including compression, shared motif extraction, cross-sequence similarity analysis, and structural visualization. Its domain-agnostic design enables broad applicability across areas such as genomics, natural language, symbolic computation, and program analysis. Beyond providing a practical approximation of complexity, Ladderpath also offers structural insight into the modular grammar of sequences, pointing to a deeper connection between algorithmic complexity and compositional hierarchies observed in real-world data.