论文标题
在广义组合网络的标量和向量解之间的差距上
On the Gap between Scalar and Vector Solutions of Generalized Combination Networks
论文作者
论文摘要
我们研究广义组合网络的标量线性和矢量线性溶液。根据网络参数和字母大小，我们在中间层中最大节点的最大节点数量上得出了新的上限和下限。这些边界改善并扩展了已知边界的参数范围。使用这些新边界，我们在最佳标量线和最佳矢量线性网络编码解决方案之间的字母大小的间隙上呈现一个下限和上限。对于固定的网络结构，在改变中层节点$ r $的数量时，上限和下限的渐近行为表明差距为$θ（\ log（r））$。
We study scalar-linear and vector-linear solutions of the generalized combination network. We derive new upper and lower bounds on the maximum number of nodes in the middle layer, depending on the network parameters and the alphabet size. These bounds improve and extend the parameter range of known bounds. Using these new bounds we present a lower bound and an upper bound on the gap in the alphabet size between optimal scalar-linear and optimal vector-linear network coding solutions. For a fixed network structure, while varying the number of middle-layer nodes $r$, the asymptotic behavior of the upper and lower bounds shows that the gap is in $Θ(\log(r))$.
