AI 中文总结
研究有向图上局部故障转移路由，通过改进算法缩小了数据包头可重写位上下界差距，给出了不同故障弧数量下所需可重写位数量，证明该方案在故障弧数量约小于节点数量时近乎最优。
AI 中文摘要
局部故障转移路由是一种即使在多条边出现故障时，也仅使用预先计算的路由表将数据包从源路由到目的地的机制。本文研究了在具有k条弧故障的有向图上，使数据包头中可重写位数量最小化的局部故障转移方案。无向图上的故障转移路由已有很多研究，而有向图方面研究较少。Van等人首次给出了有向图数据包头中可重写位的上下界，但上下界差距较大。本文主要贡献是缩小了上下界差距，给出了方案所需可重写位数量的具体结果，并表明该方案在故障弧数量约小于节点数量时近乎最优。
英文摘要
The local failover routing is a mechanism that routes a packet from a source to a destination only using pre-calculated routing tables, even when several edges fail. In this paper, we study local failover schemes that minimize the number of rewritable bits in the packet header on directed graphs with $k$-arc failures. There are many studies of failover routing on undirected graphs, and it has been investigated whether routing is possible depending on the number of bits in the packet header, the type of failure, the graph properties, etc. In contrast, there is not much research on directed graphs. Van et al.~first showed the upper and lower bounds of rewritable bits in the packet header on directed graphs. However, their results showed a large gap between the upper and lower bounds. The main contribution of this paper is to close the gap between the upper and lower bounds. Specifically, we show that our scheme can route packets with $k$ faulty arcs if the packet header has $\min(k \log ( \frac{e(2n+k-3)}{k}, 2n \log ( \frac{e(2n+k-3)}{2n})))$ rewritable bits, where $n$ is the number of nodes. Moreover, any local failover routing scheme needs $Ω(k\lceil\log\frac{n}{k}\rceil)$ rewritable bits when the number of faulty arcs is equal to or less than $\frac{3(n-1)}{8}$ and $\frac{n-1}{4}$ rewritable bits when the number of faulty arc is more than $\frac{3(n-1)}{8}$. This result means our scheme is nearly optimal when the number of faulty arcs is approximately less than the number of nodes.
Comments17 pages, 4 figures
