Minimum-Cost Network Flow with Dual Predictions

TL;DR

This paper introduces a minimum-cost network flow algorithm enhanced with dual predictions, improving efficiency through theoretical bounds and empirical validation in traffic and routing applications.

Contribution

It is the first to incorporate dual predictions into a minimum-cost flow algorithm, providing theoretical bounds and empirical validation for improved performance.

Findings

Achieves up to 12.74x speedup in traffic networks

Achieves up to 1.64x speedup in chip routing

Provides bounds on complexity based on prediction error

Abstract

Recent work has shown that machine-learned predictions can provably improve the performance of classic algorithms. In this work, we propose the first minimum-cost network flow algorithm augmented with a dual prediction. Our method is based on a classic minimum-cost flow algorithm, namely $\varepsilon$-relaxation. We provide time complexity bounds in terms of the infinity norm prediction error, which is both consistent and robust. We also prove sample complexity bounds for PAC-learning the prediction. We empirically validate our theoretical results on two applications of minimum-cost flow, i.e., traffic networks and chip escape routing, in which we learn a fixed prediction, and a feature-based neural network model to infer the prediction, respectively. Experimental results illustrate $12.74\times$ and $1.64\times$ average speedup on two applications.