具有有限循环次数的光学器件的结构--第一部分：贪婪结构
Constructions of Optical Queues With a Limited Number of Recirculations--Part I: Greedy Constructions
摘要：
在这篇由两部分组成的论文中，我们考虑了通过光开关和光纤延迟线的有限数量的再循环的光队列的SDL结构。我们表明，某些类型的光队列，包括线性压缩器，线性解压缩器，2到1 FIFO多路复用器，在一个简单的数据包路由方案和有限数量的再循环的约束下，可以转化为相应的约束下的等价整数表示问题的建设。给定$M$和$k$，在最大化最大延迟（分别，缓冲器大小），在我们的线性压缩器/解压缩器的构造中（分别地，2比1 FIFO多路复用器）等效于在$\Acal_M$中找到最优序列${\dbf^*}_1^M$的问题（分别，$\Bcal_M$）使得$B({\dbf^*}_1^M;k)=\max_{\dbf_1^M\in \Acal_M}B(\dbf_1^M;k)$（分别，$B({\dbf^*}_1^M;k)=\max_{\dbf_1^M\in \Bcal_M}B(\dbf_1^M;k)$），其中$\Acal_M$（分别，$\Bcal_M$）是在我们的线性压缩器/解压缩器（分别，2到1 FIFO多路复用器）。在第一部分中，我们提出了一类\emph{greedy}结构的线性压缩器/解压缩器和2到1 FIFO多路复用器，通过指定一个类$\Gcal_{M,k}$的序列，使$\Gcal_{M,k}\subseteq \Bcal_M\subseteq \Acal_M$和每个序列中的$\Gcal_{M,k}$是递归地获得在一个贪婪的方式。然后，我们证明了每一个最优的建设必须是一个贪婪的建设。在第二部分中，我们进一步证明了最多有两个最优结构，并给出了一个简单的算法来获得最优结构。
英文摘要：
In this two-part paper, we consider SDL constructions of optical queues with a limited number of recirculations through the optical switches and the fiber delay lines. We show that the constructions of certain types of optical queues, including linear compressors, linear decompressors, and 2-to-1 FIFO multiplexers, under a simple packet routing scheme and under the constraint of a limited number of recirculations can be transformed into equivalent integer representation problems under a corresponding constraint. Given $M$ and $k$, the problem of finding an \emph{optimal} construction, in the sense of maximizing the maximum delay (resp., buffer size), among our constructions of linear compressors/decompressors (resp., 2-to-1 FIFO multiplexers) is equivalent to the problem of finding an optimal sequence ${\dbf^*}_1^M$ in $\Acal_M$ (resp., $\Bcal_M$) such that $B({\dbf^*}_1^M;k)=\max_{\dbf_1^M\in \Acal_M}B(\dbf_1^M;k)$ (resp., $B({\dbf^*}_1^M;k)=\max_{\dbf_1^M\in \Bcal_M}B(\dbf_1^M;k)$), where $\Acal_M$ (resp., $\Bcal_M$) is the set of all sequences of fiber delays allowed in our constructions of linear compressors/decompressors (resp., 2-to-1 FIFO multiplexers). In Part I, we propose a class of \emph{greedy} constructions of linear compressors/decompressors and 2-to-1 FIFO multiplexers by specifying a class $\Gcal_{M,k}$ of sequences such that $\Gcal_{M,k}\subseteq \Bcal_M\subseteq \Acal_M$ and each sequence in $\Gcal_{M,k}$ is obtained recursively in a greedy manner. We then show that every optimal construction must be a greedy construction. In Part II, we further show that there are at most two optimal constructions and give a simple algorithm to obtain the optimal construction(s).
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