Swapped interconnection networks: Topological, performance, and robustness attributes

Biswapped Networks and Their Topological Properties

“…Note that the difference between this definition and that in [10] and [15] is that the case p = g is not excluded from the second set in the definition of E(Γ); in other words, here we postulate that the swap link associated with a node 〈p, p〉 in Sw(Ω) is a self-loop, whereas in the original definition of [10] and [15], node 〈p, p〉 lacks a swap link and thus has a node degree that is one less than that of node 〈p, g〉 with p ≠ g. The swapped network based on a regular n-node, degree-d network Ω has n 2 nodes of degree d + 1. Because the class of Cayley graphs exhibits many desirable properties and also includes a significant fraction of all networks that have been found useful in parallel processing, we next consider biswapped networks built from basis networks that are Cayley graphs.…”

“…4. The 32-node biswapped network with the basis graph Ω = C 4 is homomorphic to the 16-node swapped network using the same basis graph, with the latter being identical to its counterpart in [10] if all the self-loops are removed.…”

“…In this paper, we propose a new class of interconnection networks called "biswapped networks" (BSNs) that are related to swapped or OTIS networks, previously proposed and studied by a number of researchers [4], [7], [10], [15]. A network in the new proposed class is built of 2n copies of some n-node basis network using a simple rule for connectivity that ensures its regularity, modularity, fault tolerance, and algorithmic efficiency.…”

An Efficient Construction of Node Disjoint Paths in OTIS Networks

“…〈3,0〉 The following basis topological metrics of OTIS-Ω as functions of the corresponding metrics of Ω are derived from Definition 1 and similar expressions in [3,9]:…”

“…Although some studies are related to general properties, including fault tolerance, of OTIS networks [3,9,17,18], so far all research work in this direction is only confined to OTIS networks with basis networks being maximally fault tolerant, and those proposed constructions of parallel paths in these OTIS networks are closely dependent upon the corresponding constructions in their basis networks [2,3,9].…”