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Lumines is NP-complete: Or at least if your gamepad is broken
KTH, School of Computer Science and Communication (CSC).
KTH, School of Computer Science and Communication (CSC).
2015 (English)Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
Abstract [en]

Lumines is a popular puzzle game where the player organizes dichromatic 2 × 2 blocks on a rectangular grid by rotating and moving them around the gameboard. A line eventually sweeps the gameboard and clears all 2 × 2 monochromatic squares that the player has formed. This report examines the complexity of offline Lumines with two significant simplifications: squares are cleared instantly when formed and the player is not allowed to rotate the blocks. A decision problem is formulated for this model and shown to be in NP. The NP-complete subset sum problem is reduced to the decision problem, thereby proving the Lumines model to be NP-complete. The essence of the reduction from subset sum shows potential for further use in similiar stacking 2-dimensional puzzle games.

Place, publisher, year, edition, pages
National Category
Computer Science
URN: urn:nbn:se:kth:diva-168182OAI: diva2:814621
Available from: 2015-05-28 Created: 2015-05-27 Last updated: 2015-05-28Bibliographically approved

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