  Oblivious routing is a well-studied paradigm that uses static precomputed
routing tables for selecting routing paths within a network. Existing oblivious
routing schemes with polylogarithmic competitive ratio for general networks are
tree-based, in the sense that routing is performed according to a convex
combination of trees. However, this restriction to trees leads to a
construction that has time quadratic in the size of the network and does not
parallelize well. In this paper we study oblivious routing schemes based on
electrical routing. In particular, we show that general networks with $n$
vertices and $m$ edges admit a routing scheme that has competitive ratio
$O(\log^2 n)$ and consists of a convex combination of only $O(\sqrt{m})$
electrical routings. This immediately leads to an improved construction
algorithm with time $\tilde{O}(m^{3/2})$ that can also be implemented in
parallel with $\tilde{O}(\sqrt{m})$ depth.
