Decision algorithms for unsplittable flow and the half-disjoint paths problem
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
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
WAE '01 Proceedings of the 5th International Workshop on Algorithm Engineering
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ACM SIGCOMM Computer Communication Review
Fairness in Routing and Load Balancing
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
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STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
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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
Logarithmic hardness of the undirected edge-disjoint paths problem
Journal of the ACM (JACM)
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Computer Networks: The International Journal of Computer and Telecommunications Networking
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Half integral packing, Erdős-Posá-property and graph minors
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
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Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
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ACM SIGCOMM Computer Communication Review
On the approximation of the single source k-splittable flow problem
Journal of Discrete Algorithms
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IEEE/ACM Transactions on Networking (TON)
A nearly linear time algorithm for the half integral parity disjoint paths packing problem
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Improved algorithm for the half-disjoint paths problem
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
SecondNet: a data center network virtualization architecture with bandwidth guarantees
Proceedings of the 6th International COnference
The disjoint paths problem: algorithm and structure
WALCOM'11 Proceedings of the 5th international conference on WALCOM: algorithms and computation
Breaking o(n1/2)-approximation algorithms for the edge-disjoint paths problem with congestion two
Proceedings of the forty-third annual ACM symposium on Theory of computing
Heuristic approaches to service level agreements in packet networks
WINE'05 Proceedings of the First international conference on Internet and Network Economics
On the approximability of the minimum congestion unsplittable shortest path routing problem
IPCO'05 Proceedings of the 11th international conference on Integer Programming and Combinatorial Optimization
The disjoint paths problem in quadratic time
Journal of Combinatorial Theory Series B
ViNEYard: virtual network embedding algorithms with coordinated node and link mapping
IEEE/ACM Transactions on Networking (TON)
Slice embedding solutions for distributed service architectures
ACM Computing Surveys (CSUR)
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Computer Networks: The International Journal of Computer and Telecommunications Networking
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In the single-source unsplittable flow problem we are given a graph G, a source vertex s and a set of sinks t_1,\ldots,t_k with associated demands. We seek a single s-t_i flow path for each commodity i so that the demands are satisfied and the total flow routed across any edge e is bounded by its capacity c_e. The problem is an NP-hard variant of max flow and a generalization of single-source edge-disjoint paths with applications to scheduling, load balancing and virtual-circuit routing problems. In a significant development, Kleinberg gave recently constant-factor approximation algorithms for several natural optimization versions of the problem \cite{Kleinberg96}. In this paper we give a generic framework that yields simpler algorithms and significant improvements upon the constant factors. Our framework, with appropriate subroutines, applies to all optimization versions previously considered and treats in a unified manner directed and undirected graphs. To give a flavor of our results, consider minimizing relative congestion, i.e. the maximum ratio over all edges e of the flow through e divided by the capacity c_e. This metric was a primary testbed for randomized rounding techniques and has been studied extensively. We give a simple (3.23+o(1))-approximation algorithm for both directed and undirected graphs. The previously known bounds were 16 for the directed and 8.25 for the undirected case. Our approach also gives the first constant-factor approximation for minimum-cost unsplittable flow on directed graphs and improves considerably upon the approximation ratio for the minimum cost version on undirected graphs. The algorithmic techniques we introduce are quite general and apply to related problems as well. For example we use them to give a constructive proof of the following fact. If there exists an algorithm {\cal A} for (multisource) edge-disjoint paths such that {\cal A} outputs an approximation for relative congestion that is \rho times the fractional optimum, then a corresponding O(\rho)-approximation algorithm exists for multisource unsplittable flow with arbitrary demands and capacities. On the negative side we show that for the problem with two sources, no \rho-approximation with \rho0. We give a best possible, unless P=NP, 3/2-approximation for this restricted unsplittable flow problem and generalizations to other restricted sets of demands.