Compact Routing in Directed Networks with Stretch Factor of Two

Abstract

This paper presents a compact routing algorithm with stretch less than 3for directed networks. Although for stretch less than 3, the lower bound for the total routing information in the network is Ω(n ²) bits, it is still worth examining to determine the best possible saving in space. The routing algorithm uses header size of 4 log n and provides round-trip stretch factor of 2, while bounding the local space by $\left[ {n - \sqrt n \left( {\sqrt {{{1 - 7} \mathord{\left/ {\vphantom {{1 - 7} {4n}}} \right. \kern-\nulldelimiterspace} {4n}}} } \right) - {1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} \right]\log n$. These results for stretch less than 3for directed networks match those for undirected networks.