 
Summary: Logarithmic Hardness of the Directed Congestion
Minimization Problem
Matthew Andrews
Bell Labs, Murray Hill, NJ
andrews@research.belllabs.com
Lisa Zhang
Bell Labs, Murray Hill, NJ
ylz@research.belllabs.com
ABSTRACT
We show that for any constant # > 0, there is
no#24 1# M)
approximation algorithm for the directed congestion min
imization problem on networks of size M unless NP #
ZPT IME(n polylog n ). This bound is almost tight given the
O(log M/ log log M)approximation via randomized round
ing due to Raghavan and Thompson.
Categories and Subject Descriptors
F.2 [Analysis of Algorithms and Problem Complex
ity]: Nonnumerical Algorithms and Problems
General Terms
