Graph Coloring Using Heat Diffusion

Graph coloring is a problem with varied applications in industry and science such as scheduling, resource allocation, and circuit design. The purpose of this paper is to establish if a new gradient based iterative solver framework known as heat diffusion can solve the graph coloring problem. We propose a solution to the graph coloring problem using the heat diffusion framework. We compare the solutions against popular methods and establish the competitiveness of heat diffusion method for the graph coloring problem.

A Novel Differentiable Loss Function for Unsupervised Graph Neural Networks in Graph Partitioning

In this paper, we explore the graph partitioning problem, a pivotal combina-torial optimization challenge with extensive applications in various fields such as science, technology, and business. Recognized as an NP-hard prob-lem, graph partitioning lacks polynomial-time algorithms for its resolution. Recently, there has been a burgeoning interest in leveraging machine learn-ing, particularly approaches like supervised, unsupervised, and reinforce-ment learning, to tackle such NP-hard problems. However, these methods face significant hurdles: supervised learning is constrained by the necessity of labeled solution instances, which are often computationally impractical to obtain; reinforcement learning grapples with instability in the learning pro-cess; and unsupervised learning contends with the absence of a differentia-ble loss function, a consequence of the discrete nature of most combinatorial optimization problems. Addressing these challenges, our research introduces a novel pipeline employing an unsupervised graph neural network to solve the graph partitioning problem. The core innovation of this study is the for-mulation of a differentiable loss function tailored for this purpose. We rigor-ously evaluate our methodology against contemporary state-of-the-art tech-niques, focusing on metrics: cuts and balance, and our findings reveal that our is competitive with these leading methods.