Distributed and Fault-Tolerant Routing for Borel Cayley Graphs

Abstract

We explore the use of a pseudorandom graph family, Borel Cayley graph family, as the network topology with thousands of nodes operating in a packet switching environment. BCGs are known to be an efficient topology in interconnection networks because of their small diameters, short average path lengths, and low-degree connections. However, the application of BCGs is hindered by a lack of size flexibility and fault-tolerant routing. We propose a fault-tolerant routing algorithm for BCGs. Our algorithm exploits the vertex-transitivity property of Borel Cayley graphs and relies on extra information to reflect topology change. Our results show that the proposed method supports good reachability and a small End-to-End delay under various link failures scenarios.

Priority driven Call Scheduling in Mobile Networks: A MOGA based approach

“…Hence, the Figure 13 shows an improved performance of the proposed model over such existing approach. The use of MOGA in the proposed approach has significantly reduced computational complexity when compared with traditional search approaches used in [21]. As shown in Figure 14, the traditional model explodes exponentially when lim R is increased above a certain value, whereas the proposed approach provides constant growth even for higher values.…”

Circular slider graphs: de Bruijn, Kautz, Rauzy, lamplighters and spiders

“…In spite of a number of studies of the fault tolerance of de Bruijn and Kautz graphs to edge failures (e.g., see [RNT12], [LZL17] and the references therein), circular slider graphs other than the ones determined by various factorial languages (see Section 3) have not attracted much attention per se.…”

“…On the right of Figure 5.3 is the transversally Markov slider graph − → S Σ A 3 obtained by removing the de Bruijn transitions α 1 α 2 α 3 ∼ α 2 α 3 α 4 with α 1 = α 4 = 1. The following class of examples of transversally Markov circular slider graphs is inspired by the lamplighters (see below Section 6) and is based on the notion of the Cayley graph of a group (the use of which is currently becoming popular in the theory of interconnection networks, see [RNT12], [CPFV14]). Let us first remind that the (directed) Cayley graph (≡ Cayley topological Markov chain) − − → Cay(G, K) on a group G determined by a subset K ⊂ G has the vertex set G and the arrows g ∼ gk , g ∈ G, k ∈ K .…”