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Symphony & Small Worlds as Overlay Networks Kamil Pawlowski Kamil Pawlowski

Introduction This paper presents an experiment in running small world rings (specifically Symphony) as overlay networks on top of various base graphs/networks. The aim of the experiment is to characterize the behavior of small world rings in terms of the graphs on which they are overlaid. The over arching goal of the experiment is to gain an understanding of the applicability of small world rings in real world scenarios. In the model used by this paper nodes in the base network are said to host nodes that belong to the small world ring overlaid on top of it. Nodes in the small world ring maintain their own links (edges), but those links run over the underlying base graph. Thus navigating along the small world ring means visiting all of the base graph nodes that carry those particular ring edges. The specific focus of this paper is the number of base graph nodes that must be visited when traversing the small world ring. Shorter total paths are considered superior. This is sometimes referred to as having lower latency, or shorter distance. This paper finds that if host nodes are chosen at random, assigning small world nodes to those host nodes so that base graph distance between adjacent small world nodes is minimized, results in shorter paths than when the host node to small world node assignment is random. This paper finds that small world rings overlaid on top of data center like tree graphs have shorter total paths than those overlaid on top of random graphs, and Internet like graphs. This also paper finds that when a routing operation is performed on the overlaid ring a reasonable heuristic exists for the number of base graph nodes that are traversed during this operation. This heuristic is: Finally the paper finds that time it takes to route a message around the ring is too large for main line data center applications, and that small world rings are more likely to be useful as command and control infrastructure in datacenters.