Technical Report Number
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 is contained in DTIME(2^polylog(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+epsilon)-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.
Dartmouth Digital Commons Citation
Bansal, Nikhil; Chakrabarti, Amit; Epstein, Amir; and Schieber, Baruch, "A Quasi-PTAS for Unsplittable Flow on Line Graphs" (2005). Computer Science Technical Report TR2005-561. https://digitalcommons.dartmouth.edu/cs_tr/282