Attacking the Grid Colouring Problem with Constraint Programming

This project aims to solve the 17×17 4-colouring challenge first proposed by William Gasarch in late 2009. The challenge is to fill a 17×17 grid with four colours such that no rectangle within the grid has the same colour in all of its four corners. This is one of the few unsolved problems in grid-colouring, and it has been studied from several different perspectives since the challenge was made. Even if the problem remains unsolved, this project should a good insight into the grid-colouring problem from a constraint programming point of view. Constraint programming will be used to attack this problem, a method that has not been previously attempted in any great detail. A Constraint Satisfaction Model is built for the general 4-colouring problem, and a ground-up approach is taken; as the model is improved, it is able to find larger grid-colourings in a reasonable amount of time. Both common constraint programming techniques and properties of the problem are used to enhance the model. This project makes use of MiniZinc, a modern and succinct constraint modelling language which is able to capture the problem in a concise manner.