A tradeoff between space and efficiency for routing tables
A tradeoff between space and efficiency for routing tables
复制标题
路由表空间和效率之间的权衡
DOI：
10.1145/62212.62217
复制
发表时间：
1988
期刊：
影响因子：
--
通讯作者：
E. Upfal
中科院分区：
文献类型：
--
作者：
D. Peleg;E. Upfal
两个冲突的目标在通信网络的路由方案的设计中起着至关重要的作用。 。一对顶点。
以前的工作集中在为特殊类别的网络拓扑中找到良好的路由方案（具有较小的固定拉伸因子）路由计划的效率及其空间要求之间的权衡。 <Italic> n </Italic> - vertex网络，该网络达到拉伸因子<italic> k </italic>≥1必须使用总计＆ohgr;（<Italic> n </italic> <supscrpt> <supscrpt> 1+1+1/2 <Italic> k </italic> +4 </supscrpt>）网络中的路由信息。 <Italic>层次结构</斜体>路由方案（对于每个固定<Italic> k </italic>≥1），保证了伸展因子的伸展因子<Italic>＆ogr; </italic>（<italic> k </italic>），需要存储总计<italic>＆ogr; </italic>（<italic> n </italic> n </italic> <supscrpt> <supscrpt> 1+1+1+1/ <Italic> k </italic> </scrpt>）网络中的路由信息位，并用<Italic>＆ogr; </italic>命名顶点（log <supscrpt> 2 </supscrpt> 2 </supscrpt> <italic> <italic> n </</</</</</ i>斜体>） - 位名称。
Two conflicting goals play a crucial role in the design of routing schemes for communication networks. A routing scheme should use as short as possible paths for routing messages in the network, while keeping the routing information stored in the processors' local memory as succinct as possible. The efficiency of a routing scheme is measured in terms of its <italic>stretch factor</italic> - the maximum ratio between the length of a route computed by the scheme and that of a shortest path connecting the same pair of vertices.
Most previous work has concentrated on finding good routing schemes (with a small fixed stretch factor) for special classes of network topologies. In this work we study the problem for general networks, and look at the entire range of possible stretch factors. The results exhibit a tradeoff between the efficiency of a routing scheme and its space requirements. We present almost tight upper and lower bounds for this tradeoff. Specifically, we prove that any routing scheme for general <italic>n</italic>-vertex networks that achieves a stretch factor <italic>k</italic> ≥ 1 must use a total of &OHgr;(<italic>n</italic><supscrpt>1+1/2<italic>k</italic>+4</supscrpt>) bits of routing information in the networks. This lower bound is complemented by a family <italic>H</italic>(<italic>k</italic>) of <italic>hierarchical</italic> routing schemes (for every fixed <italic>k</italic> ≥ 1), which guarantee a stretch factor of <italic>&Ogr;</italic>(<italic>k</italic>), require storing a total of <italic>&Ogr;</italic>(<italic>n</italic><supscrpt>1+1/<italic>k</italic></supscrpt>) bits of routing information in the network and name the vertices with <italic>&Ogr;</italic>(log<supscrpt>2</supscrpt> <italic>n</italic>)-bit names.