Cayley DHTs — A Group-Theoretic Framework for Analyzing DHTs Based on Cayley Graphs

Paths to stardom

“…In parallel to the above systems, works such as that of Ratajczak and Hellerstein [29], Qu et al [28] or Gummadi et al [11], successfully argue for an analysis of the underlying static structure of the P2P overlays before looking at the algorithms implemented on top of it to deal with load balancing and churn. First, [11] presents an empirical analysis based on the simulations of various types of networks and concludes that routing geometry is fundamental and that flexibility is a key parameter.…”

“…Such a study was initiated in [29] and independently extended in [28]. Both works identify Cayley graphs as the common underlying structure of the most popular P2P overlays.…”

“…We continue the modifications and from the definition of the hypercube we define the d-torus that forms the CAN overlay: This definition improves upon earlier ones in [28,29] because it eliminates artificial distinctions between the allowable number of splits in each dimension. Previous definitions also confused the dimensionality of CAN with the dimensionality of the identifier space (note that CAN increases its identifiers based on the number of splits, not the dimensionality, which is fixed apriori).…”

“…Recently, [29] and [28] have observed that most structured overlay networks have Cayley graphs as their static architecture. These abstract algebra graphs have been studied in the late 1980s and early 1990s in the context of parallel com-puters (processor interconnection networks), but properties that are considered important in that context, like planarity -the possibility to arrange the nodes without intersecting the edges, are not relevant in P2P overlays.…”

“…We propose a new analysis for a better understanding of a graph's potential to constitute the basis of the next PDMS. Additionally, we address the proposal of [29] and [28] to use the Star graph as underlying structure and analyze it from the point of view of a PDMS.…”