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
Experimental Evaluation of Approximation Algorithms for Single-Source Unsplittable Flow
Proceedings of the 7th International IPCO Conference on Integer Programming and Combinatorial Optimization
Optimal Link Capacity Dimensioning in Proportionally Fair Networks
NETWORKING '02 Proceedings of the Second International IFIP-TC6 Networking Conference on Networking Technologies, Services, and Protocols; Performance of Computer and Communication Networks; and Mobile and Wireless Communications
On the k-Splittable Flow Problem
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
Hop-by-hop routing algorithms for premium traffic
ACM SIGCOMM Computer Communication Review
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
Approximating covering integer programs with multiplicity constraints
Discrete Applied Mathematics
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
Multicommodity flow, well-linked terminals, and routing problems
Proceedings of the thirty-seventh 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
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Information Processing Letters
Appia: Automatic Storage Area Network Fabric Design
FAST '02 Proceedings of the 1st USENIX Conference on File and Storage Technologies
Meet and merge: Approximation algorithms for confluent flows
Journal of Computer and System Sciences - Special issue on network algorithms 2005
Implementing approximation algorithms for the single-source unsplittable flow problem
Journal of Experimental Algorithmics (JEA)
Logarithmic hardness of the undirected edge-disjoint paths problem
Journal of the ACM (JACM)
A mixed-integer approach to Core-Edge design of storage area networks
Computers and Operations Research
A faster combinatorial approximation algorithm for scheduling unrelated parallel machines
Theoretical Computer Science
Degree-constrained network flows
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
(Almost) Tight bounds and existence theorems for single-commodity confluent flows
Journal of the ACM (JACM)
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IEEE/ACM Transactions on Networking (TON)
Single source multiroute flows and cuts on uniform capacity networks
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Reliable multipath provisioning for high-capacity backbone mesh networks
IEEE/ACM Transactions on Networking (TON)
A nearly linear time algorithm for the half integral disjoint paths packing
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
On the approximation of the single source k-splittable flow problem
Journal of Discrete Algorithms
Maximum Bipartite Flow in Networks with Adaptive Channel Width
ICALP '09 Proceedings of the 36th Internatilonal Collogquium on Automata, Languages and Programming: Part II
Minimum-cost single-source 2-splittable flow
Information Processing Letters
How bad is single-path routing
GLOBECOM'09 Proceedings of the 28th IEEE conference on Global telecommunications
Advanced combinatorial algorithms
Algorithms and theory of computation handbook
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
Maximum flows on disjoint paths
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Parameterized Tractability of Edge-Disjoint Paths on Directed Acyclic Graphs
SIAM Journal on Discrete Mathematics
Maximum bipartite flow in networks with adaptive channel width
Theoretical Computer Science
Appia: automatic storage area network fabric design
FAST'02 Proceedings of the 1st USENIX conference on File and storage technologies
Scheduling unrelated parallel machines computational results
WEA'06 Proceedings of the 5th international conference on Experimental Algorithms
A faster combinatorial approximation algorithm for scheduling unrelated parallel machines
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
Finding two disjoint paths in a network with normalized α+-MIN-SUM objective function
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
The disjoint paths problem in quadratic time
Journal of Combinatorial Theory Series B
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APPROX'06/RANDOM'06 Proceedings of the 9th international conference on Approximation Algorithms for Combinatorial Optimization Problems, and 10th international conference on Randomization and Computation
Capacitated confluent flows: complexity and algorithms
CIAC'10 Proceedings of the 7th international conference on Algorithms and Complexity
Evolutionary algorithm for congestion problem in connection-oriented networks
ICCSA'05 Proceedings of the 2005 international conference on Computational Science and Its Applications - Volume Part IV
Single-source k-splittable min-cost flows
Operations Research Letters
Cost of not splitting in routing: characterization and estimation
IEEE/ACM Transactions on Networking (TON)
Choosy: max-min fair sharing for datacenter jobs with constraints
Proceedings of the 8th ACM European Conference on Computer Systems
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Proceedings of the Twelfth ACM Workshop on Hot Topics in Networks
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The max-flow min-cut theorem of Ford and Fulkerson is based on an even more foundational result, namely Menger's theorem on graph connectivity Menger's theorem provides a good characterization for the following single-source disjoint paths problem: given a graph G, with a source vertex s and terminals t1,...,tk, decide whether there exist edge-disjoint s-ti paths for i=1,...,k.We consider a natural, NP-hard generalization of this problem, which we call the single-source unsplittable flow problem. We are given a source and terminals as before; but now each terminal ti has a demand pi = 1, and each edge e of G has a capacity ce = 1. The problem is to decide whether one can choose a single s-ti path for each i, so that the resulting set of paths respects the capacity constraints-the total amount of demand routed across any edge e must be bounded by the capacity ce. The main results of this paper are constant-factor approximation algorithms for three natural optimization versions of this problem, in arbitrary directed and undirected graphs. The development of these algorithms requires a number of new techniques for rounding fractional solutions to network flow problems; for two of the three problems we consider, there were no previous techniques capable of providing an approximation in the general case, and for the third, the randomized rounding algorithm of Raghavan and Thompson provides a logarithmic approximation. Our techniques are also of interest from the perspective of a family of NP-hard load balancing and machine scheduling problems that can be reduced to the single-source unsplittable flow problem.