Algorithm for Interpretable Graph Features via Motivic Persistent Cohomology

TL;DR

This paper introduces CPA, an algorithm for computing interpretable persistent cohomological features of graphs, with proven complexity bounds and practical testing on molecular graphs.

Contribution

The paper presents CPA, a novel event-driven algorithm for persistent cohomology of graphs, with theoretical complexity analysis and real-world applicability.

Findings

CPA is exponential in worst case but fixed-parameter tractable in treewidth.

CPA is nearly linear for trees, cycles, and series-parallel graphs.

Practical experiments show CPA's effectiveness on molecular-like graphs.

Abstract

We present the Chromatic Persistence Algorithm (CPA), an event-driven method for computing persistent cohomological features of weighted graphs via graphic arrangements, a classical object in computational geometry. We establish rigorous complexity results: CPA is exponential in the worst case, fixed-parameter tractable in treewidth, and nearly linear for common graph families such as trees, cycles, and series-parallel graphs. Finally, we demonstrate its practical applicability through a controlled experiment on molecular-like graph structures.