The Simultaneous Maze Solving Problem
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A grid maze is a binary matrix where fields containing a 0 are accessible while fields containing a 1 are blocked. A movement sequence consists of relative movements up, down, left, right – moving to a blocked field results in non-movement. The simultaneous maze solving problem asks for the shortest movement sequence starting in the upper left corner and visiting the lower right corner for all mazes of size n × m (for which a path from the upper left to the lower right corner exists at all). We present a theoretical problem analysis, including hardness results and a cubic upper bound on the sequence length. In addition, we describe several approaches to practically compute solving sequences and lower bounds despite the high combinatorial complexity of the problem.
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FUNKE, Stefan, Andre NUSSER, Sabine STORANDT, 2017. The Simultaneous Maze Solving Problem. Thirty-First AAAI Conference on Artificial Intelligence (AAAI-17). San Francisco, 4. Feb. 2017 - 10. Feb. 2017. In: Proceedings of the Thirty-First AAAI Conference on Artificial Intelligence. Palo Alto, California: AAAI Publications, 2017, pp. 808-814BibTex
@inproceedings{Funke2017Simul-43310, year={2017}, title={The Simultaneous Maze Solving Problem}, url={https://aaai.org/ocs/index.php/AAAI/AAAI17/paper/view/14617}, publisher={AAAI Publications}, address={Palo Alto, California}, booktitle={Proceedings of the Thirty-First AAAI Conference on Artificial Intelligence}, pages={808--814}, author={Funke, Stefan and Nusser, Andre and Storandt, Sabine} }
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