Sorting in c log n parallel steps
Combinatorica
A correction network for N-sorters
SIAM Journal on Computing
Depth optimal sorting networks resistant to k passive faults
Proceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms
ICPP '99 Proceedings of the 1999 International Conference on Parallel Processing
Sorting networks and their applications
AFIPS '68 (Spring) Proceedings of the April 30--May 2, 1968, spring joint computer conference
Research note: Networks for sorting multitonic sequences
Journal of Parallel and Distributed Computing
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In this paper we construct sorting comparator networks which correct a fixed number t of faults in a sorted sequence of length N. We study two kinds of such networks. One construction yields a fault tolerant unit that attached at the end of any comparator sorting network makes the whole network a sorting one resistant to t passive faults. The second network can be used to 'repair' a sorted sequence in which at most t entries were changed (no fault tolerance is required). The new results of this paper are constructions of comparator networks of depth 1:44ċlog N for these problems which is less than the depths of networks described by previous authors [3],[4],[5]. The construction of the networks is practical for small t. The numbers of comparators used by our networks are shown to be reducible to values optimal up to a constant factor.