Hop-Constrained Oblivious Routing

We prove the existence of an oblivious routing scheme that is -competitive in terms , thus resolving a well-known question routing. Concretely, consider undirected network and set packets each with its own source destination. The objective to choose path for packet, from destination, so as minimize defined follows: dilation maximum hop length, congestion number paths include any single edge. obliviously randomly selects packet independent (the of) other packets. Despite this obliviousness, selected have within factor best possible value. More precisely, integer constraint length at most comparison achievable via hops. These can be sampled polynomial time. This result viewed analogue celebrated results Räcke [Proceedings 43rd Annual IEEE Symposium on Foundations Computer Science, 2002; Proceedings 40th ACM Theory Computing, 2008], which are but not competitive dilation.