# Graph Colouring Meets Deep Learning: Effective Graph Neural Network Models for Combinatorial Problems

@article{Lemos2019GraphCM, title={Graph Colouring Meets Deep Learning: Effective Graph Neural Network Models for Combinatorial Problems}, author={Henrique Lemos and Marcelo O. R. Prates and Pedro H. C. Avelar and L. Lamb}, journal={2019 IEEE 31st International Conference on Tools with Artificial Intelligence (ICTAI)}, year={2019}, pages={879-885} }

Deep learning has consistently defied state-of-the-art techniques in many fields over the last decade. However, we are just beginning to understand the capabilities of neural learning in symbolic domains. Deep learning architectures that employ parameter sharing over graphs can produce models which can be trained on complex properties of relational data. These include highly relevant NP-Complete problems, such as SAT and TSP. In this work, we showcase how Graph Neural Networks (GNN) can be…

## 30 Citations

Deep Learning Chromatic and Clique Numbers of Graphs

- Computer ScienceArXiv
- 2021

Deep learning models are developed to predict the chromatic number and maximum clique size of graphs, both of which represent classical NP-complete combinatorial optimization problems encountered in graph theory.

Can Graph Neural Networks Learn to Solve MaxSAT Problem?

- Computer ScienceArXiv
- 2021

Two kinds of GNN models are built to learn the solution of MaxSAT instances from benchmarks, and it is shown that GNNs have attractive potential to solveMaxSAT problem through experimental evaluation and theoretical explanation of the effect.

Learning to solve NP-complete problems

- Computer Science
- 2019

This work shows that Graph Neural Networks are powerful enough to solve NP-Complete problems which combine symbolic and numeric data, in addition to proposing a modern reformulation of the meta-model.

Learning the Satisfiability of Pseudo-Boolean Problem with Graph Neural Networks

- Computer ScienceCP
- 2020

A GNN-based classification model to learn the satisfiability of pseudo-Boolean (PB) problem is proposed and experiments indicate that GNN has great potential in solving constraint satisfaction problems with numerical coefficients.

Computing Steiner Trees using Graph Neural Networks

- Computer ScienceArXiv
- 2021

This paper tackles the Steiner Tree Problem and suggests that the out-of-the-box application of GNN methods does worse than the classic 2-approximation method, but when combined with a greedy shortest path construction, it even does slightly better than the 2- approximation algorithm.

Combinatorial Optimization with Physics-Inspired Graph Neural Networks

- Computer Science, PhysicsArXiv
- 2021

The graph neural network optimizer performs on par or outperforms existing solvers, with the ability to scale beyond the state of the art to problems with millions of variables.

HyperGCN: A New Method For Training Graph Convolutional Networks on Hypergraphs

- Computer Science, MathematicsNeurIPS
- 2019

This work proposes HyperGCN, a novel GCN for SSL on attributed hypergraphs, and shows how it can be used as a learning-based approach for combinatorial optimisation on NP-hard hypergraph problems.

HyperGCN: Hypergraph Convolutional Networks for Semi-Supervised Classification

- Mathematics, Computer ScienceArXiv
- 2018

This work proposes HyperGCN, an SSL method which uses a layer-wise propagation rule for convolutional neural networks operating directly on hypergraphs, which is the first principled adaptation of GCNs to hyper graphs.

TilinGNN: Learning to Tile with Self-Supervised Graph Neural Network

- Computer ScienceACM Trans. Graph.
- 2020

This work introduces the first neural optimization framework to solve a classical instance of the tiling problem, and builds a graph convolutional neural network, coined TilinGNN, to progressively propagate and aggregate features over graph edges and predict tile placements.

Deep Learning-based Approximate Graph-Coloring Algorithm for Register Allocation

- 2020 IEEE/ACM 6th Workshop on the LLVM Compiler Infrastructure in HPC (LLVM-HPC) and Workshop on Hierarchical Parallelism for Exascale Computing (HiPar)
- 2020

Graph-coloring is an NP-hard problem which has a myriad of applications. Register allocation, which is a crucial phase of a good optimizing compiler, relies on graph coloring. Hence, an efficient…

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