An addressing and routing scheme based on modified Euclidean space for hexagonal networks

The addressing and routing algorithm on hexagonal networks is still an open problem so far. Although many related works have been done to resolve this problem to some extent, the properties of hexagonal networks are still not explored adequately. In this paper, we first create an oblique coordinate system and redefine the Euclidean space to address the hexagonal nodes. Then an optimal routing algorithm using vectors and angles of the redefined Euclidean space is developed. Compared with the traditional 3-directions scheme and the Cayley graph method, the proposed routing algorithm is more efficient and totally independent of the scale of networks with two-tuples addresses. We also prove that the path(s) obtained by this algorithm is always the shortest one(s).