An effective approach for achieving fault tolerance in hypercubes

Al-Tawil, Khalid; Avresky, Dimiter R.

doi:10.1109/ftpds.1994.494482

Cited by 3 publications

(1 citation statement)

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“…Expensive approaches were proposed to improve the fault tolerance of hypercube networks by using spares or by reconfiguration [17,18], such as the use of spare links and nodes [2], augmenting each node with one extra node [9], the use of multiple virtual nodes on each node for workload redistribution under faults [16], or reconfiguring the run-time system [17] in the case of faults. For a fixed number of nodes, the CUST used in [18] requires much less number of edges than a hypercube. When the number of faulty edges and their distribution still allow a tree to be formed in hypercube, reconfiguring the running application to a tree provides a continuation scheme in the presence of faults.…”

Section: Introductionmentioning

confidence: 99%

On the average distance of the hypercube tree

Alsuwaiyel

2010

International Journal of Computer Mathematics

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Given a graph G on n vertices, the total distance of G is defined as σ G = (1/2) u,v∈V (G) d (u, v), where d(u, v) is the number of edges in a shortest path between u and v. We define the d-dimensional hypercube tree T d and show that it has a minimum total distance σ (T d ) = 2σ (H d ) − n 2 = (dn 2 /2) − n 2 over all spanning trees of H d , where H d is the d-dimensional binary hypercube. It follows that the average distance of T d is μ(T d ) = 2μ(H d ) − 1 = d(1 + 1/(n − 1)) − 1.

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