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The maze routing problem is to find an optimal path between a given pair of cells on a grid plane. Lee's algorithm and its variants, probably the most widely used maze routing method, fails to work in the 4-geometry of the grid plane. Our algorithm solves this problem by using a suitable data structure for uniform wave propagation in the 4-geometry, 8-geometry, etc. The algorithm guarantees finding an optimal path if it exists and has linear time and space complexities. Next, to solve thedoi:10.1145/1044111.1044118 fatcat:g7eufvnaafc3tnlv7izg4i6jva