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
![$$
\left[ {n - \sqrt n \left( {\sqrt {{{1 - 7} \mathord{\left/
{\vphantom {{1 - 7} {4n}}} \right.
\kern-\nulldelimiterspace} {4n}}} } \right) - {1 \mathord{\left/
{\vphantom {1 2}} \right.
\kern-\nulldelimiterspace} 2}} \right]\log n
$$](/content/wy3qwt5nha54dn5e/3-540-45307-5_3_Chapter_TeX2GIFIEq1.gif)
. These results for stretch less than 3for directed networks match those for undirected networks.