  We prove the existence of an oblivious routing scheme that is
$\mathrm{poly}(\log n)$-competitive in terms of $(congestion + dilation)$, thus
resolving a well-known question in oblivious routing.
  Concretely, consider an undirected network and a set of packets each with its
own source and destination. The objective is to choose a path for each packet,
from its source to its destination, so as to minimize $(congestion +
dilation)$, defined as follows: The dilation is the maximum path hop-length,
and the congestion is the maximum number of paths that include any single edge.
The routing scheme obliviously and randomly selects a path for each packet
independent of (the existence of) the other packets. Despite this
obliviousness, the selected paths have $(congestion + dilation)$ within a
$\mathrm{poly}(\log n)$ factor of the best possible value. More precisely, for
any integer hop-bound $h$, this oblivious routing scheme selects paths of
length at most $h \cdot \mathrm{poly}(\log n)$ and is $\mathrm{poly}(\log
n)$-competitive in terms of $congestion$ in comparison to the best possible
$congestion$ achievable via paths of length at most $h$ hops. These paths can
be sampled in polynomial time.
  This result can be viewed as an analogue of the celebrated oblivious routing
results of R\"{a}cke [FOCS 2002, STOC 2008], which are $O(\log n)$-competitive
in terms of $congestion$, but are not competitive in terms of $dilation$.
