A quasi-PTAS for unsplittable flow on line graphs

We study the Unsplittable Flow Problem (UFP) on a line graph, focusing on the long-standing open question of whether the problem is APX-hard. We describe a deterministic quasi-polynomial time approximation scheme for UFP on line graphs, thereby ruling out an APX-hardness result, unless NP DTIME(2polylog(n)). Our result requires a quasi-polynomial bound on all edge capacities and demands in the input instance. Earlier results on this problem included a polynomial time (2 + )-approximation under the assumption that no demand exceeds any edge capacity (the "no-bottleneck assumption") and a super-constant integrality gap if this assumption did not hold. Unlike most earlier work on UFP, our results do not require a no-bottleneck assumption.

• Type: Conference
• Year: 2006
• Where: STOC
• Authors: Nikhil Bansal, Amit Chakrabarti, Amir Epstein, Baruch Schieber
• Keywords: Algorithms, No-bottleneck Assumption, STOC 2006, Time Approximation Scheme, Unsplittable Flow Problem