Building synchronizable and robust networks

Abstract

In this paper we present a simple, fast, novel algorithm for building networks whose topology has high synchronizability, is robust against failures, and supports efficient communication. We show that the algorithm is able to build these networks in a small number of steps that scales with the networks density. In addition, we track the evolution of different topological properties in the process of generating these networks. The results show that the topological properties are homogeneously distributed and the topology is less authoritative. Furthermore, we show that the networks we generate are more robust than random, geometric random, small-world or scalefree networks with similar average connectivity. Finally, all of the results indicate that the topology of these networks is entangled, which in many cases represents an optimal topology.

Enhancing the synchronizability of networks by rewiring based on tabu search and a local greedy algorithm

“…For example, the complexity is O(M N ) for the method suggested in Ref. [28]. However, as shown in our simulation later, its performance is poor because it may be trapped in local minima on regular networks.…”

“…[13], [24], [26], and [27] and the network rebuilding method described in Ref. [28]. Figure 3 depicts the results for the proposed algorithm with L = Q = 1 and…”

“…A similar approach for edge deletion is suggested in Ref. [28]. However, since the design concept in Ref.…”

“…However, since the design concept in Ref. [28] is based on the observation that homogeneous properties usually make a network more synchronizable, [21] edges are added to connect nodes with the lowest degrees.…”

“…To develop a relatively complete algorithm with iterative improvement, the rewiring scheme is commonly incorporated with some optimization approaches, such as simulated annealing, [12,13,21−23] greedy heuristic [25,26,28] or tabu search. [20] Unfortunately, since a global search is needed to select the "best" edges for adding or deleting, the computational complexities of the aforementioned methods are usually very high.…”