Accelerating Domain Propagation: an Efficient GPU-Parallel Algorithm over Sparse Matrices

TL;DR

This paper introduces a GPU-efficient algorithm for domain propagation in linear constraints, significantly speeding up solving processes in mixed integer programming and pseudo-boolean optimization.

Contribution

The paper presents a novel GPU-parallel algorithm for domain propagation that handles irregularities and enables entirely GPU-based propagation rounds, improving performance.

Findings

Achieves 10x to 20x geometric mean speedup on large instances

Reaches up to 180x speedup on very large instances

Demonstrates effectiveness on state-of-the-art GPUs

Abstract

Fast domain propagation of linear constraints has become a crucial component of today's best algorithms and solvers for mixed integer programming and pseudo-boolean optimization to achieve peak solving performance. Irregularities in the form of dynamic algorithmic behaviour, dependency structures, and sparsity patterns in the input data make efficient implementations of domain propagation on GPUs and, more generally, on parallel architectures challenging. This is one of the main reasons why domain propagation in state-of-the-art solvers is single thread only. In this paper, we present a new algorithm for domain propagation which (a) avoids these problems and allows for an efficient implementation on GPUs, and is (b) capable of running propagation rounds entirely on the GPU, without any need for synchronization or communication with the CPU. We present extensive computational results which demonstrate the effectiveness of our approach and show that ample speedups are possible on practically relevant problems: on state-of-the-art GPUs, our geometric mean speed-up for reasonably-large instances is around 10x to 20x and can be as high as 180x on favorably-large instances.