Information and Computation
Reliable Broadcast in Hypercube Multicomputers
IEEE Transactions on Computers
Message routing in an injured hypercube
C3P Proceedings of the third conference on Hypercube concurrent computers and applications: Architecture, software, computer systems, and general issues - Volume 1
Routing and broadcasting in faulty hypercube computers
C3P Proceedings of the third conference on Hypercube concurrent computers and applications: Architecture, software, computer systems, and general issues - Volume 1
Fast computation using faulty hypercubes
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Tolerating Faults in Hypercubes Using Subcube Partitioning
IEEE Transactions on Computers - Special issue on fault-tolerant computing
Combinatorial Algorithms: Theory and Practice
Combinatorial Algorithms: Theory and Practice
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We consider the problem of computing a global commutative and associative operation, also known as semi-group operation, (such as addition and multiplication) on a faulty hypercube. In particular, we study the problem of performing such an operation in an n-dimensional SIMD hypercube, Qn, with up to n驴 1 node and/or link faults. In an SIMD hypercube, during a communication step, nodes can exchange information with their neighbors only across a specific dimension.Given a set of at most n驴 1 faults, we develop an ordering d1, d2, ..., dn of n dimensions, depending on where the faults are located. An important and useful property of this dimension ordering is the following: if the n-cube is partitioned into k-subcubes using the first k dimensions of this ordering, namely d1, d2, ... dk for any 2 驴k驴n, then each k-subcube in the partition contains at most k驴 1 faults. We use this result to develop algorithms for global sum. These algorithms use 3n驴 2, n + 3 log n + 3 log log n, and n + log n + 4 log log n + O(log log log n) time steps, respectively.