Recently, there has been a lot of attention on the constructions of optical queues by using optical Switches and fiber Delay Lines (SDL). In this paper, we consider the constructions of optical queues with a limited number of recirculations through the fibers in such SDL constructions. Such a limitation on the number of recirculations comes from practical feasibility considerations, such as crosstalk, power loss, amplified spontaneous emission (ASE) from the Erbium doped fiber amplifiers (EDFA), and the pattern effect of the optical switches. We first transform the design of the fiber delays in such SDL constructions to an equivalent integer representation problem. Specifically, given 1 <= k <= M, we seek for an M-sequence d_(1)~(M) velence (d_(1),d_(2),...,d_(M)) of positive integers to maximize the number of consecutive integers (starting from 0) that can be represented by the C-transform relative to d_(1)~(M) such that there are at most k 1-entries in their C-transforms. Then we give a class of greedy constructions so that d_(1), d_(2),...,d_(M) are obtained recursively and the maximum number of representable consecutive integers by using d_(1), d_(2),..., d_(i) is larger than that by using d_(1), d_(2),..., d_(i-1) for all i. Furthermore, we obtain an explicit recursive expression for d_(1), d_(2),..., d_(M) given by a greedy construction. Finally, we show that an optimal M-sequence (in the sense of achieving the maximum number of representable consecutive integers) can be given by a greedy construction. The solution of such an integer representation problem can be applied to the construction of optical 2-to-1 FIFO multiplexers with a limited number of recirculations. We show that the complexity of searching for an optimal construction under our routing policy can be greatly reduced from exponential time to polynomial time by only considering the greedy constructions instead of performing an exhaustive search. Similar results can be obtained for linear compressors and linear decompressors with a limited number of recirculations.
展开▼
机译：最近，通过使用光学开关和光纤延迟线（SDL）对光学队列的结构存在很大的注意。在本文中，我们考虑通过这种SDL结构中的纤维具有有限数量的再循环的光学队列的结构。对循环次数的许多限制来自实际可行性考虑因素，例如串扰，功率损耗，来自铒掺杂光纤放大器（EDFA）的串扰，以及光学开关的图案效果。我们首先将这种SDL结构中的光纤延迟的设计转换为等同的整数表示问题。具体地，给定1 <= k <= m，我们寻求正整数的m-sequence d_（1）〜（m）velence（d_（1），d_（2），...，d_（m））为了最大化可以由相对于D_（1）〜（m）表示的C变换表示的连续整数（从0开始），使得其C变换中的大多数k 1条条目。然后我们给出一类贪婪的结构，以便通过使用d_（1），d_（2）递归地获得D_（1），d_（2），...，d_（m），并且通过d_（1），d_（2）递归地获得最大可表示的连续整数数，......，d_（i）比使用d_（1），d_（2），...，d_（i-1）来大得多。此外，我们获得了由贪婪建设给出的D_（1），d_（2），...，d_（m）的显式递归表达式。最后，我们表明可以通过贪婪的结构给出最佳的M序列（在实现最大表示的连续整数的最大数量）。这种整数表示问题的解决方案可以应用于具有有限数量的再循环的光学2至1 FIFO多路复用器的结构。我们表明，在我们的路由策略下搜索最佳结构的复杂性可以通过仅考虑贪婪的结构而不是执行详尽的搜索来从指数时间到多项式时间来大大减少到多项式时间。可以获得类似的结果，用于线性压缩机和具有有限数量的再循环的线性减压器。
展开▼
