Periodic comparator networks

Periodic comparator networks

We survey recent results on periodic algorithms. We focus on the problems of sorting, merging and permuting and concentrate on algorithms that have small constant periods.

Comparator Networks for Binary

Reliable Minimum Finding Comparator Networks

We consider the problem of constructing reliable minimum nd-ing networks built from unreliable comparators. In case of a faulty compara-tor inputs are directly output without comparison. Our main result is the rst nontrivial lower bound on depths of networks computing minimum among n > 2 items in the presence of k > 0 faulty comparators. We prove that the depth of any such network is at least m...

Comparator Networks for Binary Heap Construction

Comparator networks for constructing binary heaps of size n are presented which have size O(n log log n) and depth O(log n). A lower bound of n log log n ?O(n) for the size of any heap construction network is also proven, implying that the networks presented are within a constant factor of optimal. We give a tight relation between the leading constants in the size of selection networks and in t...

Optimal Conclusive Sets for Comparator Networks

A set of input vectors S is conclusive for a certain functionality if, for every comparator network, correct functionality for all input vectors is implied by correct functionality for all vectors in S. We consider four functionalities of comparator networks: sorting, merging, sorting of bitonic vectors, and halving. For each of these functionalities, we present two conclusive sets of minimal c...