Embedding Algorithms for Bubble-Sort, Macro-star, and Transposition Graphs

Abstract

Abstract. Bubble-sort, macro-star, and transposition graphs are interconnection networks with the advantages of star graphs in terms of improving the network cost of a hypercube. These graphs contain a star graph as their sub-graph, and have node symmetry, maximum fault tolerance, and recursive partition properties. This study proposes embedding methods for these graphs based on graph definitions, and shows that a bubble-sort graph B n can be embedded in a transposition graph T n with dilation 1 and expansion 1. In contrast, a macro-star graph MS(2, n) can be embedded in a transposition graph with dilation n, but with an average dilation of 2 or under.

An Algorithm for One-to-One Mapping Matrix-star Graph into Transposition Graph

“…It is also a node symmetry and bipartite graph. It has maximum fault tolerance because its diameter is n-1, fault diameter is n, and node connectivity is equal to the number of its degree n(n-1)/2 [2,8]. Fig.…”

“…Therefore, the need to further develop interconnection networks is continuously growing with the development of parallel processing computers [8]. Most research on interconnection networks has focused on evaluating the parameters for measuring the performance of networks, including degree, diameter, fault tolerance, embedding, broadcasting, symmetry, and scalability [1,9].…”