Maximally Local Connectivity on Augmented Cubes

  • Authors:

  • Y-Chuang Chen;Meng-Hung Chen;Jimmy J. Tan

  • Affiliations:

  • Department of Information Management, Ming Hsin University of Science and Technology, Hsin Feng, Hsinchu 304, Taiwan, R.O.C.;Department of Computer Science, National Chiao Tung University, Hsinchu, Taiwan, R.O.C. 300;Department of Computer Science, National Chiao Tung University, Hsinchu, Taiwan, R.O.C. 300

  • Venue:
  • ICA3PP '09 Proceedings of the 9th International Conference on Algorithms and Architectures for Parallel Processing
  • Year:
  • 2009

Quantified Score

Hi-index 0.00

Visualization

Abstract

Connectivity is an important measurement for the fault tolerance in interconnection networks. It is known that the augmented cube AQ n is maximally connected , i.e. (2n - 1)-connected, for n *** 4. By the classical Menger's Theorem , every pair of vertices in AQ n is connected by 2n - 1 vertex-disjoint paths for n *** 4. A routing with parallel paths can speed up transfers of large amounts of data and increase fault tolerance. Motivated by some research works on networks with faults, we have a further result that for any faulty vertex set F *** V (AQ n ) and |F | ≤ 2n *** 7 for n *** 4, each pair of non-faulty vertices, denoted by u and v , in AQ n *** F is connected by min{deg f (u ), deg f (v )} vertex-disjoint fault-free paths, where deg f (u ) and deg f (v ) are the degree of u and v in AQ n *** F , respectively. Moreover, we have another result that for any faulty vertex set F *** V (AQ n ) and |F | ≤ 4n *** 9 for n *** 4, there exists a large connected component with at least 2 n *** |F | *** 1 vertices in AQ n *** F . In general, a remaining large fault-free connected component also increases fault tolerance.