Theory of linear and integer programming
Theory of linear and integer programming
Randomized rounding: a technique for provably good algorithms and algorithmic proofs
Combinatorica - Theory of Computing
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
On the inapproximability of disjoint paths and minimum Steiner forest with bandwidth constraints
Journal of Computer and System Sciences
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
ICALP '93 Proceedings of the 20th International Colloquium on Automata, Languages and Programming
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
Faster and Simpler Algorithms for Multicommodity Flow and other Fractional Packing Problems.
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Multicommodity Flow and Circuit Switching
HICSS '98 Proceedings of the Thirty-First Annual Hawaii International Conference on System Sciences-Volume 7 - Volume 7
Approximating Directed Multicuts
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Approximation algorithms for disjoint paths problems
Approximation algorithms for disjoint paths problems
A note on the greedy algorithm for the unsplittable flow problem
Information Processing Letters
Graph decomposition and a greedy algorithm for edge-disjoint paths
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
New hardness results for congestion minimization and machine scheduling
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
The all-or-nothing multicommodity flow problem
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Approximate max-integral-flow/min-multicut theorems
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
Approximation algorithms for cycle packing problems
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Hardness of the Undirected Edge-Disjoint Paths Problem with Congestion
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
A quasi-PTAS for unsplittable flow on line graphs
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
On the max-flow min-cut ratio for directed multicommodity flows
Theoretical Computer Science
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)
Improved bounds for the unsplittable flow problem
Journal of Algorithms
Hardness of routing with congestion in directed graphs
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Single source multiroute flows and cuts on uniform capacity networks
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Approximation algorithms and hardness results for cycle packing problems
ACM Transactions on Algorithms (TALG)
Disjoint paths in sparse graphs
Discrete Applied Mathematics
Approximability of packing disjoint cycles
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
Proceedings of the forty-second ACM symposium on Theory of computing
K-Tree: A multiple tree video multicast protocol for Ad hoc wireless networks
Computer Networks: The International Journal of Computer and Telecommunications Networking
A nature-inspired algorithm for the disjoint paths problem
IPDPS'06 Proceedings of the 20th international conference on Parallel and distributed processing
Edge Disjoint Paths in Moderately Connected Graphs
SIAM Journal on Computing
Disjoint cycles: integrality gap, hardness, and approximation
IPCO'05 Proceedings of the 11th international conference on Integer Programming and Combinatorial Optimization
Edge disjoint paths in moderately connected graphs
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
Greedy approximation via duality for packing, combinatorial auctions and routing
MFCS'05 Proceedings of the 30th international conference on Mathematical Foundations of Computer Science
Approximation algorithms for edge-disjoint paths and unsplittable flow
Efficient Approximation and Online Algorithms
Routing in undirected graphs with constant congestion
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Operations Research Letters
On the complexity and approximation of the min-sum and min-max disjoint paths problems
ESCAPE'07 Proceedings of the First international conference on Combinatorics, Algorithms, Probabilistic and Experimental Methodologies
Hi-index | 0.00 |
The approximability of the maximum edge disjoint paths problem (EDP) in directed graphs was seemingly settled by the Ω(m1/2-ε)-hardness result of Guruswami et al. [10] and the O(√m) approximation achievable via both the natural LP relaxation [19] and the greedy algorithm [11, 12]. Here m is the number of edges in the graph. However, we observe that the hardness of approximation shown in [10] applies to sparse graphs and hence when expressed as a function of n, the number of vertices, only an Ω(n1/2-ε)-hardness follows. On the other hand, the O(√m)-approximation algorithms do not guarantee a sub-linear (in terms of n) approximation algorithm for dense graphs. We note that a similar gap exists in the known results on the integrality gap of the natural LP relaxation: an Ω(√n) lower bound and an O(√m) upper bound. Motivated by this discrepancy in the upper and lower bounds we study algorithms for the EDP in directed and undirected graphs obtaining improved approximation ratios. We show that the greedy algorithm has an approximation ratio of O(min(n2/3, √m)) in undirected graphs and a ratio of O(min(n4/5, √m)) in directed graphs. For ayclic graphs we give an O(√n log n) approximation via LP rounding. These are the first sub-linear approximation ratios for EDP. Our results also extend to EDP with weights and to the unsplittable flow problem with uniform edge capacities.