Delay Optimized Small-World Networks

Many regular networks suffer from significant network delay due to large end-to-end hop distance among source nodes and destination nodes in the network. However, the presence of a few long-ranged links transforms a regular network to a small-world network, and thus, optimizes network delay by minimizing end-to-end hop distance. In this paper, we study various deterministic long-ranged link addition strategies (e.g., based on average path length, average edge length, betweenness centrality, closeness centrality, and closeness centrality disparity) to incorporate small-world characteristics as well as to optimize average network delay of the network. Moreover, we analyze time complexity to assess the efficiency of each strategy in detail. We observe, in an $N$ node network, that deterministic long-ranged link addition by closeness centrality disparity (CCD) strategy is only ${\cal O}(N^{2}\times\log N)$ time complex compared to other optimal long-ranged link addition strategies which take ${\cal O}(N^{4}\times\log N)$ time to achieve similar performance in the context of average network delay.