Broadcasting secure messages via optimal independent spanning trees in folded hypercubes

  • Authors:

  • Jinn-Shyong Yang;Hung-Chang Chan;Jou-Ming Chang

  • Affiliations:

  • Institute of Information Science and Management, National Taipei College of Business, Taipei, Taiwan, ROC;Department of Computer Science and Information Engineering, Yuanpei University, Hsinchu, Taiwan, ROC;Institute of Information Science and Management, National Taipei College of Business, Taipei, Taiwan, ROC

  • Venue:
  • Discrete Applied Mathematics
  • Year:
  • 2011

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Abstract

Fault-tolerant broadcasting and secure message distribution are important issues for network applications. It is a common idea to design multiple spanning trees with a specific property in the underlying graph of a network to serve as a broadcasting scheme or a distribution protocol for receiving high levels of fault-tolerance and security. An n-dimensional folded hypercube, denoted by FQ"n, is a strengthening variation of hypercube by adding additional links between nodes that have the furthest Hamming distance. In, [12], Ho(1990) proposed an algorithm for constructing n+1 edge-disjoint spanning trees each with a height twice the diameter of FQ"n. Yang et al. (2009), [29] recently proved that Ho's spanning trees are indeed independent, i.e., any two spanning trees have the same root, say r, and for any other node vr, the two different paths from v to r, one path in each tree, are internally node-disjoint. In this paper, we provide another construction scheme to produce n+1 independent spanning trees of FQ"n, where the height of each tree is equal to the diameter of FQ"n plus one. As a result, the heights of independent spanning trees constructed in this paper are shown to be optimal.