Embedding algorithms for star, bubble-sort, rotator-faber-moore, and pancake graphs

Authors:
Mihye Kim;Dongwan Kim;Hyeongok Lee
Affiliations:
Department of Computer Science Education, Catholic University of Daegu, Gyeonsansi, Gyeongbuk, South Korea;Department of Computer Education, Sunchon National University, Suncheon, Chonnam, South Korea;Department of Computer Education, Sunchon National University, Suncheon, Chonnam, South Korea
Venue:
ICA3PP'10 Proceedings of the 10th international conference on Algorithms and Architectures for Parallel Processing - Volume Part II
Year:
2010

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Abstract

Star, bubble-sort, pancake, and Rotator-Faber-Moore (RFM) graphs are well-known interconnection networks that have node symmetric, maximum fault tolerance and hierarchical partition properties. These graphs are widely assumed to improve the network cost of a hypercube. This study proposes embedding methods for a star graph and its variations, and provides an analysis of the relevant costs. Results show that a bubble-sort graph can be embedded in a star graph with dilation 3, and in a RFM graph with dilation 2, while a star graph can be embedded in a pancake graph with dilation 4. The results suggest that the embedding method developed for the bubble-sort graph can be simulated in star graphs and RFM graphs in constant time O(1).