# GPU-based Ising Computing for Solving Balanced Min-Cut Graph Partitioning Problem

## TL;DR

This paper introduces a GPU-accelerated Ising computing approach with a novel model and algorithm to efficiently solve the balanced min-cut graph partitioning problem, outperforming existing tools in quality.

## Contribution

It proposes the Global Decoupled Ising (GDI) model and an annealing algorithm that improve efficiency and scalability for balanced min-cut problems on GPUs.

## Key findings

- Outperforms METIS in partition quality on G-set benchmarks
- Maintains similar CPU/GPU times as existing methods
- Effectively handles global balance constraints without full connectivity

## Abstract

Ising computing provides a new computing paradigm for many hard combinatorial optimization problems. Ising computing essentially tries to solve the quadratic unconstrained binary optimization problem, which is also described by the Ising spin glass model and is also the basis for so-called Quantum Annealing computers. In this work, we propose a novel General Purpose Graphics Processing Unit (GPGPU) solver for the balanced min-cut graph partitioning problem, which has many applications in the area of design automation and others. Ising model solvers for the balanced min-cut partitioning problem have been proposed in the past. However, they have rarely been demonstrated in existing quantum computers for many meaningful problem sizes. One difficulty is the fact that the balancing constraint in the balanced min-cut problem can result in a complete graph in the Ising model, which makes each local update a global update. Such global update from each GPU thread will diminish the efficiency of GPU computing, which favors many localized memory accesses for each thread. To mitigate this problem, we propose an novel Global Decoupled Ising (GDI) model and the corresponding annealing algorithm, in which the local update is still preserved to maintain the efficiency. As a result, the new Ising solver essentially eliminates the need for the fully connected graph and will use a more efficient method to track and update global balance without sacrificing cut quality. Experimental results show that the proposed Ising-based min-cut partitioning method outperforms the state of art partitioning tool, METIS, on G-set graph benchmarks in terms of partitioning quality with similar CPU/GPU times.