Abstract
Nintendo’s Mario Kart is perhaps the most popular racing video game franchise. Players race alone or against opponents to finish in the fastest time possible. Players can also use items to attack and defend from other racers. We prove two hardness results for generalized Mario Kart: deciding whether a driver can finish a course alone in some given time is \(\mathrm {NP}\)-hard, and deciding whether a player can beat an opponent in a race is \(\mathrm {PSPACE}\)-hard.
E. Waingarten—Work performed while at MIT.
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Notes
- 1.
We conjecture that implementations model the position and velocity vector of a player by floating-point numbers, discretize time into fixed-duration intervals, and model the track by a collection of succinctly describable segments and turns. For a sufficiently fine discretization of time, this model should approach our continuous model. To compute the optimal traversal time of a constant-complexity track, we can finitely sample the position/velocity space and search the resulting state graph. We conjecture that a polynomial-resolution sampling suffices to approximate the optimal traversal time to the needed \(1+O(1/n^c)\) accuracy for our reductions.
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Bosboom, J., Demaine, E.D., Hesterberg, A., Lynch, J., Waingarten, E. (2016). Mario Kart Is Hard. In: Akiyama, J., Ito, H., Sakai, T., Uno, Y. (eds) Discrete and Computational Geometry and Graphs. JCDCGG 2015. Lecture Notes in Computer Science(), vol 9943. Springer, Cham. https://doi.org/10.1007/978-3-319-48532-4_5
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DOI: https://doi.org/10.1007/978-3-319-48532-4_5
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