STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Improved bounds for the unsplittable flow problem
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Experimental Evaluation of Approximation Algorithms for Single-Source Unsplittable Flow
Proceedings of the 7th International IPCO Conference on Integer Programming and Combinatorial Optimization
Meet and merge: approximation algorithms for confluent flows
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Fairness in Routing and Load Balancing
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Journal of Computer and System Sciences
The all-or-nothing multicommodity flow problem
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
(Almost) tight bounds and existence theorems for confluent flows
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Computing Nash equilibria for scheduling on restricted parallel links
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Hardness of the undirected edge-disjoint paths problem
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Meet and merge: Approximation algorithms for confluent flows
Journal of Computer and System Sciences - Special issue on network algorithms 2005
Improved bounds for the unsplittable flow problem
Journal of Algorithms
Efficient load-balancing routing for wireless mesh networks
Computer Networks: The International Journal of Computer and Telecommunications Networking
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Let $G=(V,E)$ be a capacitated directed graph with a source $s$ and $k$ terminals $t_i$ with demands $d_i$, $1\le i\le k$. 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.