Applied Graph Theory

Effective algorithm for finding shortest paths in dense Gaussian networks

E. A. Monakhova, O. G. Monakhov

Institute of Computational Mathematics and Mathematical Geophysics SB RAS, Novosibirsk, Russia

Abstract: As a promising topology of networks on a chip, we consider a family of Dense Gaussian Networks, which are optimal circulant degree four graphs of the form $C(D^2+(D+1)^2; D, D+1)$. For this family, an algorithm for finding the shortest paths between graph vertices is proposed, which uses relative addressing of vertices and, unlike a number of the known algorithms, allows to calculate the shortest paths without using the coordinates of neighboring lattice zeros in a dense tessellation of graphs on the $\mathbb{Z}^2$ plane. This reduces the memory and execution time costs compared to other algorithms when the new algorithm is implemented on a network-on-chip with a Dense Gaussian Network topology.

Keywords: Dense Gaussian Networks, circulant graphs, shortest paths, networks on a chip.

UDC: 519.87

DOI: 10.17223/20710410/58/9

Bibliographic databases:

•