Abstract
In this paper we have studied fault tolerance of a full binary tree in terms of availability of non-faulty (full) subtrees. When an unaugmented full binary tree is faulty, then the computation can be carried out on the largest available non-faulty (full) binary subtree.
It is shown that the minimum number of faulty nodes required to destroy all subtrees of height h in a full binary tree of height n is given as fbt(n, h)=⌎(2n−1)/(2h−1)⌏. It follows that the availability of a non-faulty subtree of height h=n−w, in an n level full binary tree containing u faulty nodes, can be ensured, where w is the smallest integer such that u≤2w.
An algorithm which evaluates whether a given set of faulty nodes will destroy all subtrees of some specified height, is given. This algorithm can also evaluate the largest available non-faulty subtree in a faulty full binary tree. We also study the availability of a non-faulty subtree in some augmented binary tree architectures.
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© 1991 Springer-Verlag Berlin Heidelberg
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Mittal, R., Jain, B.N., Patney, R.K. (1991). Subtree availability in binary tree architectures. In: Dehne, F., Fiala, F., Koczkodaj, W.W. (eds) Advances in Computing and Information — ICCI '91. ICCI 1991. Lecture Notes in Computer Science, vol 497. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-54029-6_179
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DOI: https://doi.org/10.1007/3-540-54029-6_179
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