NP-completeness of the game Kingdomino

Viet-Ha Nguyen; Kevin Perrot; Mathieu Vallet

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arXiv · 1909.02849

NP-completeness of the game Kingdomino

Viet-Ha Nguyen·Kevin Perrot·Mathieu Vallet

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Abstract

Kingdomino is a board game designed by Bruno Cathala and edited by Blue Orange since 2016. The goal is to place $2 \times 1$ dominoes on a grid layout, and get a better score than other players. Each $1 \times 1$ domino cell has a color that must match at least one adjacent cell, and an integer number of crowns (possibly none) used to compute the score. We prove that even with full knowledge of the future of the game, in order to maximize their score at Kingdomino, players are faced with an NP-complete optimization problem.

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Viet-Ha Nguyen, Kevin Perrot, Mathieu Vallet. 2019-09-06. NP-completeness of the game Kingdomino. https://arxiv.org/abs/1909.02849

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