TY - JOUR

T1 - On the single-source unsplittable flow problem

AU - Dinitz, Yefim

AU - Garg, Naveen

AU - Goemans, Michel X.

N1 - Funding Information:
Mathematics Subject Classi cation (1991): 90B10, 90C35, 05C38, 05C85. * This work was done when the author was on leave at the Max-Planck Institut für Informatik, Saarbrücken, Germany from Department of Computer Science, Technion, Haifa, Israel. yThis research was done while the author was at the Max-Planck-Institut für Informatik, Saarbrücken and was supported by the EU ESPRIT LTR Project No. 20244 (ALCOM-IT). zOn leave from MIT. The research of this author was supported in part by NSF contract 9623859-CCR.

PY - 1999/1/1

Y1 - 1999/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0009679463&partnerID=8YFLogxK

U2 - 10.1007/s004930050043

DO - 10.1007/s004930050043

M3 - Article

AN - SCOPUS:0009679463

VL - 19

SP - 17

EP - 41

JO - Combinatorica

JF - Combinatorica

SN - 0209-9683

IS - 1

ER -