更快的3周期合并网络

摘要：

我们考虑在一个重复使用的比较器网络上合并两个排序序列的问题，也就是说，如果输出没有排序，则使用输出作为输入再次应用网络。具有挑战性的任务是构建这种小深度的网络。具有恒定周期的合并网络的第一个构造是由Kutykowski，Lorykowski和Oesterdikhoff给出的。他们给出了$3$ -周期性网络，合并两个排序序列的$N$号码的时间$12\log N$和一个类似的网络周期$4$，工作在$5.67\log N$。我们提出了一个新的家庭这样的网络，是基于Canfield和Williamson定期排序。我们的$3$ -周期性合并网络在时间上界为$6\log N$。这种构造可以很容易地推广到运行时间减少的更大的恒定周期，例如，$4$ -在$4\log N$的时间上限内工作的周期性周期。此外，为了获得事实，我们引入了一种新的证明技术。

英文摘要：

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 Kutyłowski, Loryś 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.

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