  In the oblivious buy-at-bulk network design problem in a graph, the task is
to compute a fixed set of paths for every pair of source-destinations in the
graph, such that any set of demands can be routed along these paths. The
demands could be aggregated at intermediate edges where the fusion-cost is
specified by a canonical (non-negative concave) function $f$. We give a novel
algorithm for planar graphs which is oblivious with respect to the demands, and
is also oblivious with respect to the fusion function $f$. The algorithm is
deterministic and computes the fixed set of paths in polynomial time, and
guarantees a $O(\log n)$ approximation ratio for any set of demands and any
canonical fusion function $f$, where $n$ is the number of nodes. The algorithm
is asymptotically optimal, since it is known that this problem cannot be
approximated with better than $\Omega(\log n)$ ratio. To our knowledge, this is
the first tight analysis for planar graphs, and improves the approximation
ratio by a factor of $\log n$ with respect to previously known results.
