Fast methods for designing circulant network topology with high connectivity and survivability

Abstract

This paper proposes two fast methods to design network topologies with high connectivity and survivability based on circulant graph theory. The first method, namely, the Combination Method (CM), investigates the average distances of circulant graphs with different combinations of chordal jumps, and tries to locate the optimal one among them. For this purpose, empirical formulas are proposed to describe the fluctuation features of average distances on curved surfaces. Furthermore, an enhanced Local Search Method (LSM) is proposed to find the local minimum points in troughs of the surfaces. The second method, namely, the Spider Web Method (SWM), is based on a bionic concept deriving from observation of the spider web, which is a classical example of network connectivity and survivability in natural world. The relation between CM and SWM in certain situations is also discussed. Finally, the connectivity and survivability of the topologies designed by CM and SWM are verified via simulated experiments involving vertex destruction.