比率为4的丢弃成本和波长最优两周期疏导
Drop cost and wavelength optimal two-period grooming with ratio 4
摘要：
我们研究疏导两个周期的光网络，一个变化的WDM环形网络的流量疏导问题介绍了Colbourn，Quattrocchi，和Syrotiuk。在两周期疏导问题中，在第一时间段期间，在$n$节点之间存在全对全均匀业务，每个请求使用带宽的$1/C$;并且在第二时间段期间，仅在$v$节点的子集$V$之间存在全对全均匀业务，每个请求现在被允许使用带宽的$1/C'$，其中$C' < C$。我们确定任何$n,v$和C=4和$C' \in \{1,2,3\}$的最小丢弃成本（ADM的最小数量）。为此，我们使用图分解工具。实际上，两阶段梳理问题对应于最小化将完全图$K_n$的边划分为子图中的顶点总数，其中每个子图最多具有$C$条边，并且其中它还包含完全图在$v$指定顶点上的最多$C'$条边。在两个周期的疏导具有最小的丢弃成本的条件下，在每种情况下所需的波长的最小数量也被确定。
英文摘要：
We study grooming for two-period optical networks, a variation of the traffic grooming problem for WDM ring networks introduced by Colbourn, Quattrocchi, and Syrotiuk. In the two-period grooming problem, during the first period of time, there is all-to-all uniform traffic among $n$ nodes, each request using $1/C$ of the bandwidth; and during the second period, there is all-to-all uniform traffic only among a subset $V$ of $v$ nodes, each request now being allowed to use $1/C'$ of the bandwidth, where $C' < C$. We determine the minimum drop cost (minimum number of ADMs) for any $n,v$ and C=4 and $C' \in \{1,2,3\}$. To do this, we use tools of graph decompositions. Indeed the two-period grooming problem corresponds to minimizing the total number of vertices in a partition of the edges of the complete graph $K_n$ into subgraphs, where each subgraph has at most $C$ edges and where furthermore it contains at most $C'$ edges of the complete graph on $v$ specified vertices. Subject to the condition that the two-period grooming has the least drop cost, the minimum number of wavelengths required is also determined in each case.
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