Randomized rounding: a technique for provably good algorithms and algorithmic proofs
Combinatorica - Theory of Computing
An O(log k) Approximate Min-Cut Max-Flow Theorem and Approximation Algorithm
SIAM Journal on Computing
SIAM Journal on Computing
Approximations for the disjoint paths problem in high-diameter planar networks
Journal of Computer and System Sciences
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
A PCP characterization of NP with optimal amortized query complexity
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Approximation Algorithms for Disjoint Paths and Related Routing and Packing Problems
Mathematics of Operations Research
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Strongly Polynomial Algorithms for the Unsplittable Flow Problem
Proceedings of the 8th International IPCO Conference on Integer Programming and Combinatorial Optimization
ICALP '93 Proceedings of the 20th International Colloquium on Automata, Languages and Programming
Simple analysis of graph tests for linearity and PCP
Random Structures & Algorithms
Disjoint paths in densely embedded graphs
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
Improved approximations for edge-disjoint paths, unsplittable flow, and related routing problems
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Approximation algorithms for disjoint paths problems
Approximation algorithms for disjoint paths problems
Graph decomposition and a greedy algorithm for edge-disjoint paths
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
The all-or-nothing multicommodity flow problem
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Edge-Disjoint Paths in Planar Graphs
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
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
Hardness of the undirected congestion minimization problem
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Logarithmic hardness of the directed congestion minimization problem
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
A quasi-PTAS for unsplittable flow on line graphs
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Edge-disjoint paths in Planar graphs with constant congestion
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
New hardness results for congestion minimization and machine scheduling
Journal of the ACM (JACM)
Logarithmic hardness of the undirected edge-disjoint paths problem
Journal of the ACM (JACM)
Truthful unsplittable flow for large capacity networks
Proceedings of the nineteenth annual ACM symposium on Parallel algorithms and architectures
Hardness of routing with congestion in directed graphs
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Multicommodity demand flow in a tree and packing integer programs
ACM Transactions on Algorithms (TALG)
Approximation algorithms and hardness results for cycle packing problems
ACM Transactions on Algorithms (TALG)
A Preemptive Algorithm for Maximizing Disjoint Paths on Trees
SWAT '08 Proceedings of the 11th Scandinavian workshop on Algorithm Theory
Almost-tight hardness of directed congestion minimization
Journal of the ACM (JACM)
A logarithmic approximation for unsplittable flow on line graphs
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Max-Weight Integral Multicommodity Flow in Spiders and High-Capacity Trees
Approximation and Online Algorithms
Complexity of wavelength assignment in optical network optimization
IEEE/ACM Transactions on Networking (TON)
Unsplittable Flow in Paths and Trees and Column-Restricted Packing Integer Programs
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
Disjoint paths in sparse graphs
Discrete Applied Mathematics
Truthful unsplittable flow for large capacity networks
ACM Transactions on Algorithms (TALG)
Approximability of packing disjoint cycles
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
The edge disjoint paths problem in Eulerian graphs and 4-edge-connected graphs
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Edge Disjoint Paths in Moderately Connected Graphs
SIAM Journal on Computing
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
Finding multiple induced disjoint paths in general graphs
Information Processing Letters
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Edge disjoint paths in moderately connected graphs
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
Operations Research Letters
Distributed algorithms for scheduling on line and tree networks
PODC '12 Proceedings of the 2012 ACM symposium on Principles of distributed computing
An O(log n)-Approximation Algorithm for the Edge-Disjoint Paths Problem in Eulerian Planar Graphs
ACM Transactions on Algorithms (TALG)
A logarithmic approximation for unsplittable flow on line graphs
ACM Transactions on Algorithms (TALG)
On the admission of dependent flows in powerful sensor networks
IEEE/ACM Transactions on Networking (TON)
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In the Edge-Disjoint Paths problem with Congestion (EDPwC), we are given a graph with n nodes, a set of terminal pairs and an integer c. The objective is to route as many terminal pairs as possible, subject to the constraint that at most c demands can be routed through any edge in the graph. When c = 1, the problem is simply referred to as the Edge-Disjoint Paths (EDP) problem. In this paper, we study the hardness of EDPwC in undirected graphs. We obtain an improved hardness result for EDP, and also show the first polylogarithmic integrality gaps and hardness of approximation results for EDPwC. Specifically, we prove that EDP is (\log ^{\frac{1}{2} - {\rm E}} n)-hard to approximate for any constant \varepsilon 0, unless NP \subseteq ZPTIME(n^{poly\log n} ).We also show that for any congestion c = o(log log n/ log log log n), there is no (Log^{\frac{{1 - 5}}{{c + 1}}} n) approximation algorithm for EDPwC, unless NP\subseteqZPTIME(npolylog n).For larger congestion, where c = o(log log n/ log log log n) for some constant n, we obtain superconstant inapproximability ratios. All of our hardness results can be converted into integrality gaps for the multicommodity flow relaxation. We also present a separate elementary direct proof of this integrality gap result. Finally, we note that similar results can be obtained for the All-or-Nothing Flow (ANF) problem, a relaxation of EDP, in which the flow unit routed between the source-sink pairs does not have follow a single path, so the resulting flow is not necessarily integral. Using standard transformations, our results also extend to the node-disjoint versions of these problems as well as to the directed setting.