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Constructions of Optical Queues With a Limited Number of Recirculations--Part I: Greedy Constructions | | Jay Cheng
; Cheng-Shang Chang
; Sheng-Hua Yang
; Tsz-Hsuan Chao
; Duan-Shin Lee
; Ching-Min Lien
; | | Date: |
23 Apr 2010 | | Abstract: | 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 $B({dbf^*}_1^M;k)=max_{dbf_1^Min
Acal_M}B(dbf_1^M;k)$ (resp., $B({dbf^*}_1^M;k)=max_{dbf_1^Min
Bcal_M}B(dbf_1^M;k)$), 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 $Gcal_{M,k}subseteq Bcal_Msubseteq
Acal_M$ 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). | | Source: | arXiv, 1004.4070 | | Services: | Forum | Review | PDF | Favorites | |
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