AAAI Publications, Thirty-First AAAI Conference on Artificial Intelligence

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The Simultaneous Maze Solving Problem
Stefan Funke, Andre Nusser, Sabine Storandt

Last modified: 2017-02-12


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.


conformant planning; maze; universal traversal sequence; solving sequence

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