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Greedy Constructions of Optical Queues With a Limited Number of Recirculations

机译：循环次数有限的光学队列的贪婪构造

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One of the main problems in all-optical packet-switched networks is the lack of optical buffers, and currently the only known feasible technology for the constructions of optical buffers is to use optical crossbar Switches and fiber Delay Lines (SDLs). In this paper, we consider SDL constructions of optical queues with a limited number of recirculations through the optical switches and the fiber delay lines. Such a problem arises from practical feasibility considerations, such as crosstalk, power loss, amplified spontaneous emission from the Erbium doped fiber amplifiers, and the pattern effect of the optical switches. We first transform the design of the fiber delays in such SDL constructions into an equivalent integer representation problem. Specifically, given 1≤k≤M , we seek for an M -sequence dM=(d1,d2,…,dM) of positive integers to maximize the number of consecutive integers (starting from 0) that can be represented by the C -transform (a generalization of the well-known binary representation) with respect to dM such that there are at most k 1-entries in their C -transforms. Then, we propose a class of greedy constructions of dM , in which d1,d2,…,dM are obtained recursively in a greedy manner so that the number of representable consecutive integers by using d1,d2,…,di is larger than that by using d1,d2,…,di−1 for all i . Finally, we show that every optimal construction (in the sense of maximizing the number of representable consecutive integers) must be a greedy construction. As a result, the complexity of searching for an optimal construction can be greatly reduced from exponential time to polynomial time by only considering the greedy constructions rather than performing an exhaustive search. The solution of such an integer representation problem can be applied to the constructions of optical 2-to-1 FIFO multiplexers with a limited number of recirculations. Similar results can be obtained for the constructions of optical linear compressors/decompressors with a limited number of recirculations.
机译：全光分组交换网络中的主要问题之一是缺少光学缓冲器，并且目前唯一已知的用于构造光学缓冲器的可行技术是使用光学纵横开关和光纤延迟线（SDL）。在本文中，我们考虑通过光开关和光纤延迟线进行有限次数再循环的光队列的SDL构造。出现此问题的原因是实际可行的考虑因素，例如串扰，功率损耗，掺amplifier光纤放大器的放大自发发射以及光开关的图案效应。我们首先将这种SDL结构中的光纤延迟设计转换为等效的整数表示问题。具体来说，给定1≤k≤M，我们寻求一个正整数的M序列dM =（d1，d2，…，dM）以最大化可以由C-表示的连续整数（从0开始）的数量。相对于dM的变换（众所周知的二进制表示形式的概括），使得它们的C变换中最多有k个1项。然后，我们提出了一类dM的贪心构造，其中d1，d2，…，dM以贪婪的方式递归获得​​，因此使用d1，d2，…，di可表示的连续整数的数目大于对所有i使用d1，d2，...，di-1。最后，我们表明，每个最佳构造（就最大程度上表示可表示的连续整数的意义而言）都必须是贪婪的构造。结果，通过仅考虑贪婪的构造而不是进行详尽的搜索，可以从指数时间到多项式时间极大地减少寻找最佳构造的复杂度。这种整数表示问题的解决方案可以应用于循环次数有限的光学2比1 FIFO多路复用器的构造。对于具有有限数量的再循环的光学线性压缩器/解压缩器的构造，可以获得类似的结果。

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