# Almost-tight hardness of directed congestion minimization

• Published 2008 in J. ACM

#### Abstract

Given a set of demands in a directed graph, the <i>directed congestion minimization</i> problem is to route every demand with the objective of minimizing the heaviest load over all edges. We show that for any constant &epsiv; &gt; 0, there is no &#937;(log<sup>1&minus;&epsiv;</sup> <i>M</i>)-approximation algorithm on networks of size <i>M</i> unless <i>NP</i> &#8838; <i>ZPTIME</i>(<i>n</i><sup>polylog <i>n</i></sup>). This bound is almost tight given the <i>O</i>(log <i>M</i>/log log <i>M</i>)-approximation via randomized rounding due to Raghavan and Thompson.

DOI: 10.1145/1455248.1455251

### Cite this paper

@article{Andrews2008AlmosttightHO, title={Almost-tight hardness of directed congestion minimization}, author={Matthew Andrews and Lisa Zhang}, journal={J. ACM}, year={2008}, volume={55}, pages={27:1-27:20} }