Warm-starting Push-Relabel

Sami Davies, Sergei Vassilvitskii, Yuyan Wang

Keywords: algorithms with predictions, max flow, beyond worst-case analysis

TL;DR: We provide the first theoretical guarantees for seeding the Push-Relabel algorithm with a predicted flow, and we validate this theory by showing speed ups empirically.

Abstract: Push-Relabel is one of the most celebrated network flow algorithms. Maintaining a pre-flow that saturates a cut, it enjoys better theoretical and empirical running time than other flow algorithms, such as Ford-Fulkerson. In practice, Push-Relabel is even faster than what theoretical guarantees can promise, in part because of the use of good heuristics for seeding and updating the iterative algorithm. However, it remains unclear how to run Push-Relabel on an arbitrary initialization that is not necessarily a pre-flow or cut-saturating. We provide the first theoretical guarantees for warm-starting Push-Relabel with a predicted flow, where our learning-augmented version benefits from fast running time when the predicted flow is close to an optimal flow, while maintaining robust worst-case guarantees. Interestingly, our algorithm uses the gap relabeling heuristic, which has long been employed in practice, even though prior to our work there was no rigorous theoretical justification for why it can lead to run-time improvements. We then show our algorithmic framework works well in practice, as our warm-start version of Push-Relabel improves over the cold-start version by a larger and larger percentage as the size of the image increases.

Primary Area: Optimization (convex and non-convex, discrete, stochastic, robust)

Submission Number: 7536