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.

翻译：我们提出了一种事件驱动的算法——色持久性算法（CPA），该算法通过图形配置（计算几何中的经典对象）来计算加权图的持久上同调特征。我们建立了严格的复杂度结果：CPA在最坏情况下是指数级的，在树宽参数下是固定参数可处理的，并且对于常见图族（如树、环和串并联图）几乎是线性的。最后，我们通过对类分子图结构的受控实验，证明了其实际应用价值。