Mondrian Art Problem Solver

Authors

• Natalia García-Colín (garciacolin.natalia@gmail.com)
• Dimitri Leemans (leemans.dimitri@ulb.be)
• Mia Müßig (nienna@miamuessig.de)
• Érika Roldán (erika.roldan@ma.tum.de) https://www.erikaroldan.net/

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Overview

Zero Defect

• mondrian.jl: Backtracking with top-left-heuristic to check if a defect of 0 for a given n is possible. Single- and Multi-threaded functions are available.
• Old/mondrian-ideas.jl: Alternative approaches using Integer Programming and Knuth's Dancing Links algorithm which tend to be slower in practise.

Minimal Defect

• mondrian-defect.jl: Parallelized search for the minimal defect of a given n using Integer Programming and Backtracking
• Old/mondrian-defect/mondrian.jl: Alternative approaches which tend to be slower in practise.

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License

This project is licensed under the MIT License - see LICENSE file for details. If you use this code for academic purposes, please cite the paper:

Natalia García-Colín, Dimitri Leemans, Mia Müßig, and Érika Roldán, There is no perfect Mondrian partition for squares of side lengths less than 1001, Discrete Applied Mathematics Vol. 359, https://doi.org/10.1016/j.dam.2024.09.021, 2024.