Learning-augmented maximum flow

We propose a framework for speeding up maximum flow computation by using predictions. A prediction is a flow, i.e., an assignment of non-negative flow values to edges, which satisfies the flow conservation property, but does not necessarily respect the edge capacities of the actual instance (since t...

Full description

Saved in:
Bibliographic Details
Published in:Information processing letters Vol. 186; p. 106487
Main Authors: Polak, Adam, Zub, Maksym
Format: Journal Article
Language:English
Published: Elsevier B.V 01.08.2024
Subjects:
Algorithms with predictions
Analysis of algorithms
Combinatorial optimization
Maximum flow
Combinatorial optimization
Analysis of algorithms
Algorithms with predictions
Maximum flow
ISSN:0020-0190, 1872-6119
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We propose a framework for speeding up maximum flow computation by using predictions. A prediction is a flow, i.e., an assignment of non-negative flow values to edges, which satisfies the flow conservation property, but does not necessarily respect the edge capacities of the actual instance (since these were unknown at the time of learning). We present an algorithm that, given an m-edge flow network and a predicted flow, computes a maximum flow in O(mη) time, where η is the ℓ1 error of the prediction, i.e., the sum over the edges of the absolute difference between the predicted and optimal flow values. Moreover, we prove that, given an oracle access to a distribution over flow networks, it is possible to efficiently PAC-learn a prediction minimizing the expected ℓ1 error over that distribution. Our results fit into the recent line of research on learning-augmented algorithms, which aims to improve over worst-case bounds of classical algorithms by using predictions, e.g., machine-learned from previous similar instances. So far, the main focus in this area was on improving competitive ratios for online problems. Following Dinitz et al. (2021) [6], our results are among the firsts to improve the running time of an offline problem. •We speed up maximum flow computation in graphs by using predictions.•Prediction is a flow satisfying flow conservation but not necessarily capacities.•We show that such predictions are efficiently learnable.•We compute flow in O(mη) time in m-edge graphs for predictions with L1 error up to η.
ISSN:0020-0190
1872-6119
DOI:10.1016/j.ipl.2024.106487