Shuffle vs. Kautz/De Bruijn Logical Topologies for Multihop Networks: a Throughput Comparison

Abstract

This paper deals with the analysis of the throughput performance of various logical topologies for Multihop Networks. In particular, ShuffleNets, De Bruijn graphs and Kautz graphs are analyzed. For the comparison, routing algorithms adopting minimum path length are considered. A hot-spot traffic scenario is adopted, modeling the presence of a centralized network resource to which a quota of the internal traffic is directed or originated from. The analysis is carried out by varying the traffic unbalance degree, from a uniform traffic distribution to a completely unbalanced one (all the traffic is concentrated in the hot-spot node).For ShuffleNets, simple analytical expressions of the actual throughput limits are utilized. In the case of De Bruijn and Kautz graphs, instead, a lower bound of the throughput is utilized, which coincides with the actual throughput in a wide range of values of the network size.The results obtained show that Shuffle and Kautz graphs always outperform De Bruijn topologies. Moreover, ShuffleNets present a further advantage on the other topologies; in fact, since the nodes are topologically equivalent, the placement of the hot-spot node does not affect the throughput performance.

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“…An interesting class of digraphs is the so-called lexicographic digraph class [30], which includes the de Bruijn and Kautz digraphs. 1 de Bruijn digraphs have asymptotically optimal graph diameter and average node distance [29].…”

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“…An interesting class of digraphs are the lexicographic digraphs, which include the de Bruijn and Kautz digraphs (Bernabei et al, 1996) 2 . de Bruijn graphs have asymptotically optimal graph diameter and average node distance (Loguinov, 2003).…”