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Advanced Spikes `n' Stuff: An NP-Hard Puzzle Game in Which All Tutorials Are Efficiently Solvable

Authors Christian Ikenmeyer , Dylan Khangure

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Christian Ikenmeyer
  • University of Warwick, UK
Dylan Khangure
  • University of Warwick, UK

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Christian Ikenmeyer and Dylan Khangure. Advanced Spikes `n' Stuff: An NP-Hard Puzzle Game in Which All Tutorials Are Efficiently Solvable. In 12th International Conference on Fun with Algorithms (FUN 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 291, pp. 18:1-18:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.FUN.2024.18

Abstract

We adjust Alan Hazelden’s 2017 polynomial time solvable puzzle game Spikes `n' Stuff: We obtain the NP-complete puzzle game Advanced Spikes `n' Stuff with 3 trap types so that each strict subset of the traps results in a polynomial time solvable puzzle game. We think of this as a "hard game in which all tutorial levels are easy". The polynomial time algorithms for solving the tutorial games turn out to be quite different to each other.
While numerous papers analyze the complexity of games and which game objects make a game NP-hard, our paper is the first to study a game where the NP-hardness can only be achieved by a combination of all game objects, assuming P differs from NP.

Subject Classification

ACM Subject Classification
  • Theory of computation → Problems, reductions and completeness
Keywords
  • computational complexity
  • P vs NP
  • motion planning
  • games

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References

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