1 research outputs found
Counting of Shortest Paths in Cubic Grid
The enumeration of shortest paths in cubic grid is presented here. The cubic
grid considers three neighborhods--- 6-neighborhood (face connectivity),
18-neighborhood (edge connectivity), and 26-neighborhood (vertex connectivity).
The formulation for distance metrics are given here. , , and
are the three metrics for 6-neighborhood, 18-neighborhood, and
26-neighborhood. The problem is to find the number of shortest paths based on
neighborhoods between two given points in 3D cubic grid represented by
coordinate triplets. The formulation for the three neighborhoods are presented
here. This problem has theoretical importance and practical aspects.Comment: 15 pages, 8 figure