Efficient Dynamic MaxFlow Computation on GPUs

TL;DR

This paper introduces two GPU algorithms for efficiently computing max flow in dynamic graphs, handling incremental and decremental updates simultaneously, and demonstrates significant speedups over static approaches for small updates.

Contribution

The paper presents novel GPU-based algorithms for dynamic max flow that efficiently process both capacity increases and decreases in real-world graphs.

Findings

Dynamic recomputation outperforms static GPU max flow for small updates.

Algorithms effectively handle both edge capacity increments and decrements.

Real-world graph experiments validate the efficiency of the proposed methods.

Abstract

Maxflow is a fundamental problem in graph theory and combinatorial optimisation, used to determine the maximum flow from a source node to a sink node in a flow network. It finds applications in diverse domains, including computer networks, transportation, and image segmentation. The core idea is to maximise the total flow across the network without violating capacity constraints on edges and ensuring flow conservation at intermediate nodes. The rapid growth of unstructured and semi-structured data has motivated the development of parallel solutions to compute MaxFlow. However, due to the higher computational complexity, computing Maxflow for real-world graphs is time-consuming in practice. In addition, these graphs are dynamic and constantly evolve over time. In this work, we propose two Push-Relabel based algorithms for processing dynamic graphs on GPUs. The key novelty of our algorithms is their ability to efficiently handle both increments and decrements in edge capacities together when they appear in a batch. We illustrate the efficacy of our algorithms with a suite of real-world graphs. Overall, we find that for small updates, dynamic recomputation is significantly faster than a static GPU-based Maxflow.