Journal of Computer and System Sciences
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Information Processing Letters
Information Processing Letters
Learning tetris using the noisy cross-entropy method
Neural Computation
On the complexity of Katamari Damacy
Crossroads
Learners, Technology and the Brain
USAB '08 Proceedings of the 4th Symposium of the Workgroup Human-Computer Interaction and Usability Engineering of the Austrian Computer Society on HCI and Usability for Education and Work
Apply ant colony optimization to Tetris
Proceedings of the 11th Annual conference on Genetic and evolutionary computation
Computational Complexity of Cast Puzzles
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
On the evolution of artificial Tetris players
CIG'09 Proceedings of the 5th international conference on Computational Intelligence and Games
FUN'07 Proceedings of the 4th international conference on Fun with algorithms
CG'06 Proceedings of the 5th international conference on Computers and games
The complexity of flood filling games
FUN'10 Proceedings of the 5th international conference on Fun with algorithms
Approximate Dynamic Programming via a Smoothed Linear Program
Operations Research
Reducing the learning time of tetris in evolution strategies
EA'11 Proceedings of the 10th international conference on Artificial Evolution
Using informative behavior to increase engagement in the tamer framework
Proceedings of the 2013 international conference on Autonomous agents and multi-agent systems
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In the popular computer game of Tetris, the player is given a sequence of tetromino pieces and must pack them into a rectangular gameboard initially occupied by a given configuration of filled squares; any completely filled row of the gameboard is cleared and all pieces above it drop by one row. We prove that in the offline version of Tetris, it is NP-complete to maximize the number of cleared rows, maximize the number of tetrises (quadruples of rows simultaneously filled and cleared), minimize the maximum height of an occupied square, or maximize the number of pieces placed before the game ends. We furthermore show the extreme inapproximability of the first and last of these objectives to within a factor of p1-Ɛ, when given a sequence of p pieces, and the inapproximability of the third objective to within a factor of 2-Ɛ, for any Ɛ 0. Our results hold under several variations on the rules of Tetris, including different models of rotation, limitations on player agility, and restricted piecesets.