On the single-source unsplittable flow problem

Yefim Dinitz, Naveen Garg, Michel X. Goemans

Research output: Contribution to journalConference articlepeer-review

34 Scopus citations

Abstract

Let G = (V, E) be a capacitated directed graph with a source s and k terminals ti with demands di, 1≤i≤k. We would like to concurrently route every demand on a single path from s to the corresponding terminal without violating the capacities. There are several interesting and important variations of this unsplittable flow problem. If the necessary cut condition is satisfied, we show how to compute an unsplittable flow satisfying the demands such that the total flow through any edge exceeds its capacity by at most the maximum demand. For graphs in which all capacities are at least the maximum demand, we therefore obtain an unsplittable flow with congestion at most 2, and this result is best possible. Furthermore, we show that all demands can be routed unsplittably in 5 rounds, i.e all demands can be collectively satisfied by the union of 5 unsplittable flows. Finally, we show that 22.6% of the total demand can be satisfied unsplittably. These results are extended to the case when the cut condition is not necessarily satisfied. We derive a 2-approximation algorithm for congestion, a 5-approximation algorithm for the number of rounds and a 4.43 = 1/0.226-approximation algorithm for the maximum routable demand.

Original languageEnglish
Pages (from-to)290-299
Number of pages10
JournalAnnual Symposium on Foundations of Computer Science - Proceedings
StatePublished - 1 Dec 1998
EventProceedings of the 1998 39th Annual Symposium on Foundations of Computer Science - Palo Alto, CA, USA
Duration: 8 Nov 199811 Nov 1998

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