Methods for distributed unicast in hypercubes

  • Authors:

  • Hossam M. A. Fahmy;Abu_Bakr A. ElHefnawy

  • Affiliations:

  • Department Computer Engineering and Systems, Faculty of Engineering, Ain Shams University, Abdou Pacha Square, Abbassiah, Cairo, 11381, Egypt;Department Computer Engineering and Systems, Faculty of Engineering, Ain Shams University, Abdou Pacha Square, Abbassiah, Cairo, 11381, Egypt

  • Venue:
  • Journal of Systems Architecture: the EUROMICRO Journal
  • Year:
  • 2003

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Abstract

Unicast algorithms in off-line routing have been used for one-to-one communication between a source node and a destination node in an n-dimensional hypercube, denoted as Hn. A node is called k-safe, where 0 ≤ k ≤ n, if it has at least k healthy neighbors, and Hn is called k-safe if every node in it is k-safe. A k-safe Hn is connected if the number of faulty nodes, |F|, does not exceed 2k(n - k) - 1. In this paper, we propose two methods for distributed routing. The first method has been presented in [Proc. 7th Int. IEEE Conf. Electron., Circ. Syst., Jounieh, Lebanon, December, 2000, p. 194]. The second method that has not been addressed before, can be used for off-line routing. In the case of off-line routing we avoid the cost of collecting global information about the faulty nodes, and the cost of getting information about Hn, whether it is k-safe or not. The minimum requirements of the proposed methods is to have the path between the source and the destination connected. Hence, they may work when Hn is disconnected, which is an important advantage. The time cost of the first method may be O(mn4), and the expected length of the routing path between source and destination may be O(mn5), where 1 ≤ m ≤ n. The time cost of the second method may be O(enn/2), the space cost may be O(enn/2), and the expected length of the routing path between source and destination may be d(s, t).