Randomized rounding: a technique for provably good algorithms and algorithmic proofs
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Introduction to parallel algorithms and architectures: array, trees, hypercubes
Introduction to parallel algorithms and architectures: array, trees, hypercubes
Further algorithmic aspects of the local lemma
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Decision algorithms for unsplittable flow and the half-disjoint paths problem
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Online computation and competitive analysis
Online computation and competitive analysis
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Multicommodity max-flow min-cut theorems and their use in designing approximation algorithms
Journal of the ACM (JACM)
Approximation Algorithms for Disjoint Paths and Related Routing and Packing Problems
Mathematics of Operations Research
Simple on-line algorithms for the maximum disjoint paths problem
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Universal Routing Strategies for Interconnection Networks
Universal Routing Strategies for Interconnection Networks
Disjoint paths in densely embedded graphs
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
Improved Approximation Algorithms for Unsplittable Flow Problems
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Improved approximations for edge-disjoint paths, unsplittable flow, and related routing problems
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On the Single-Source Unsplittable Flow Problem
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Short paths in expander graphs
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Approximation algorithms for disjoint paths problems
Approximation algorithms for disjoint paths problems
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A note on the greedy algorithm for the unsplittable flow problem
Information Processing Letters
The all-or-nothing multicommodity flow problem
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Crossing number, pair-crossing number, and expansion
Journal of Combinatorial Theory Series B
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Short length Menger's theorem and reliable optical routing
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Single source multiroute flows and cuts on uniform capacity networks
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
The maximum edge-disjoint paths problem in complete graphs
Theoretical Computer Science
A Simple Greedy Algorithm for the k-Disjoint Flow Problem
TAMC '09 Proceedings of the 6th Annual Conference on Theory and Applications of Models of Computation
Disjoint paths in sparse graphs
Discrete Applied Mathematics
Convex combinations of single source unsplittable flows
ESA'07 Proceedings of the 15th annual European conference on Algorithms
Distributed averaging via lifted Markov chains
IEEE Transactions on Information Theory
Approximation strategies for routing edge disjoint paths in complete graphs
SIROCCO'06 Proceedings of the 13th international conference on Structural Information and Communication Complexity
New algorithms for the unsplittable flow problem
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ICCS'06 Proceedings of the 6th international conference on Computational Science - Volume Part I
Euclidean prize-collecting steiner forest
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ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
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Approximation algorithms for edge-disjoint paths and unsplittable flow
Efficient Approximation and Online Algorithms
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
Paths of bounded length and their cuts: Parameterized complexity and algorithms
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On the admission of dependent flows in powerful sensor networks
IEEE/ACM Transactions on Networking (TON)
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In this paper we consider the unsplittable flow problem (UFP): given a directed or undirected network G = (V, E) with edge capacities and a set of terminal pairs (or requests) with associated demands, find a subset of the pairs of maximum total demand for which a single flow path can be chosen for each pair so that for every edge, the sum of the demands of the paths crossing the edge does not exceed its capacity. We study the UFP both in the offline (all requests are given from the beginning) and the online (requests arrive at the system one after the other) setting. For this we introduce a new graph parameter, the flow number. With the help of the flow number we develop a general method for transforming arbitrary multicommodity flow solutions into solutions that use short paths only, generalizing a theorem of Leighton and Rao [17]. Both the parameter and the method may therefore be of independent interest. They allow us to prove upper bounds on the approximation ratio and competitive ratio of algorithms for the UFP that are significantly below all previous upper bounds.