Embedding algorithms for bubble-sort, macro-star, and transposition graphs

Authors:
HyeongOk Lee;Hyun Sim;JungHyun Seo;Mihye Kim
Affiliations:
Department of Computer Education & Engineering, Sunchon National University, Suncheon, Chonnam, South Korea;Department of Computer Education & Engineering, Sunchon National University, Suncheon, Chonnam, South Korea;Jeonnam Technopark, Suncheon, Chonnam, South Korea;Department of Computer Science Education, Catholic University of Daegu, Gyeongbuk, South Korea
Venue:
NPC'10 Proceedings of the 2010 IFIP international conference on Network and parallel computing
Year:
2010

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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 Bn can be embedded in a transposition graph Tn 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.