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Durham University

Computer Science

Profile

Publication details for Professor Iain Stewart

Stewart, I.A. (2013). Multiswapped networks and their topological and algorithmic properties. Journal of Computer and System Sciences 79(8): 1269-1286.

Author(s) from Durham

Abstract

We generalise the biswapped network Bsw(G)Bsw(G) to obtain a multiswapped network Msw(H;G)Msw(H;G), built around two graphs G and H. We show that the network Msw(H;G)Msw(H;G) lends itself to optoelectronic implementation and examine its topological and algorithmic. We derive the length of a shortest path joining any two vertices in Msw(H;G)Msw(H;G) and consequently a formula for the diameter. We show that if G has connectivity κ⩾1κ⩾1 and H has connectivity λ⩾1λ⩾1 where λ⩽κλ⩽κ then Msw(H;G)Msw(H;G) has connectivity at least κ+λκ+λ, and we derive upper bounds on the (κ+λ)(κ+λ)-diameter of Msw(H;G)Msw(H;G). Our analysis yields distributed routing algorithms for a distributed-memory multiprocessor whose underlying topology is Msw(H;G)Msw(H;G). We also prove that if G and H are Cayley graphs then Msw(H;G)Msw(H;G) need not be a Cayley graph, but when H is a bipartite Cayley graph then Msw(H;G)Msw(H;G) is necessarily a Cayley graph.