Number of Minimal Paths in a Honeycomb Grid

Abstract

The computation to find the number of minimal-length paths from a point to other in honeycomb grid is presented in this paper. There are three kinds of neighborhood used in the honeycomb grid. We solve the shortest-path counting problem for two of the neighborhoods: in case of ]- and 2-neighborhoods, given the coordinate triplets of the two points, closed formulae are proven. The case of 3-neighborhood is also considered, as well as a brief discussion is also stated for the counting the minimal paths in other grids. The number of minimal paths in isometric grid is also proposed here. The problem has theoretical aspects and can be applied in networking and in digital image processing.