Faster 3-Periodic Merging Networks

We consider the problem of merging two sorted sequences on a comparator network that is used repeatedly, that is, if the output is not sorted, the network is applied again using the output as input. The challenging task is to construct such networks of small depth. The first constructions of merging networks with a constant period were given by Kuty{\l}owski, Lory\'s and Oesterdikhoff. They have given $3$-periodic network that merges two sorted sequences of $N$ numbers in time $12\log N$ and a similar network of period $4$ that works in $5.67\log N$. We present a new family of such networks that are based on Canfield and Williamson periodic sorter. Our $3$-periodic merging networks work in time upper-bounded by $6\log N$. The construction can be easily generalized to larger constant periods with decreasing running time, for example, to $4$-periodic ones that work in time upper-bounded by $4\log N$. Moreover, to obtain the facts we have introduced a new proof technique

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. (orig.)Available from TIB Hannover: RR 6673(47) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

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. Keywords periodic network, compare-exchange operation, comparator, sorting, merging, permutation routing, switch, shift 1 Introduction We consider algorithms of a special kind designed for simple networks consisting of weak processing units. We concentrate on one feature, namely periodicity, that makes such algorithms easy to implement. We consider so called comparator networks that are typically used for tasks such as sorting, merging of sorted sequences and selection. Below we recall two alternative definitions of comparator networks: The model: Comparator networks are traditionally defined as consisting of n wires connected by comparators (see Fig. 1). The n input items move on the wires from left to 0 1 2 3 Fig. 1. A comparator network with 3 parallel steps right. At each time there is exactly one item on eac..