Incremental Strongly Connected Components with Predictions

TL;DR

This paper introduces a machine learning-informed data structure for efficiently maintaining strongly connected components in a dynamic graph, leveraging predictions to improve performance.

Contribution

It presents a novel learned data structure for incremental SCC that adapts to prediction accuracy, achieving near-optimal bounds and practical improvements.

Findings

Algorithm performs well with accurate predictions

Performance degrades gracefully with prediction errors

Empirical results confirm theoretical runtime improvements

Abstract

Algorithms with predictions is a growing area that aims to leverage machine-learned predictions to design faster beyond-worst-case algorithms. In this paper, we use this framework to design a learned data structure for the incremental strongly connected components (SCC) problem. In this problem, the $n$ vertices of a graph are known a priori and the $m$ directed edges arrive over time. The goal is to efficiently maintain the strongly connected components of the graph after each insert. Our algorithm receives a possibly erroneous prediction of the edge sequence and uses it to precompute partial solutions to support fast inserts. We show that our algorithm achieves nearly optimal bounds with good predictions and its performance smoothly degrades with the prediction error. We also implement our data structure and perform experiments on real datasets. Our empirical results show that the theory is predictive of practical runtime improvements.