IEEE Transactions on Computers
A Multiway Merge Sorting Network
IEEE Transactions on Parallel and Distributed Systems
The asymptotic complexity of merging networks
Journal of the ACM (JACM)
Sorting networks and their applications
AFIPS '68 (Spring) Proceedings of the April 30--May 2, 1968, spring joint computer conference
A generalization of the 0--1 principle for sorting
Information Processing Letters
On the complexity of min-max sorting networks
Information Sciences: an International Journal
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A set of input vectors S is conclusive if correct functionality for all input vectors is implied by correct functionality over vectors in S. We consider four functionalities of comparator networks: sorting, merging of two equal length sorted vectors, sorting of bitonic vectors, and halving (i.e., separating values above and below the median). For each of these functionalities, we present tight lower and upper bounds on the size of conclusive sets. Bounds are given both for conclusive sets composed of binary vectors and of general vectors. The bounds for general vectors are smaller than the bounds for binary vectors implied by the 0-1 principle. Our results hold also for comparator networks with unbounded fanout. Assume the network at hand has n inputs and outputs, where n is even. We present a conclusive set for sorting that contains (n n/2) nonbinary vectors. For merging, we present a conclusive set with n/2 + 1 nonbinary vectors. For bitonic sorting, we present a conclusive set with n nonbinary vectors. For halving, we present (n n/2) binary vectors that constitute a conclusive set. We prove that all these conclusive sets are optimal.