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
Probabilistic construction of deterministic algorithms: approximating packing integer programs
Journal of Computer and System Sciences - 27th IEEE Conference on Foundations of Computer Science October 27-29, 1986
Randomized algorithms
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
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
Approximation algorithms for disjoint paths problems
Approximation algorithms for disjoint paths problems
Exact and approximation algorithms for network flow and disjoint-path problems
Exact and approximation algorithms for network flow and disjoint-path problems
A note on the greedy algorithm for the unsplittable flow problem
Information Processing Letters
Journal of Computer and System Sciences
Graph decomposition and a greedy algorithm for edge-disjoint paths
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Approximating Directed Multicuts
Combinatorica
ACM Transactions on Algorithms (TALG)
Minimum-cost multiple paths subject to minimum link and node sharing in a network
IEEE/ACM Transactions on Networking (TON)
Approximation algorithms for orienting mixed graphs
Theoretical Computer Science
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The approximability of the maximum edge-disjoint paths problem (EDP) in directed graphs was seemingly settled by an Ω(m1/2 − &epsis;)-hardness result of Guruswami et al. [2003], and an O(&sqrt;m) approximation achievable via a natural multicommodity-flow-based LP relaxation as well as a greedy algorithm. Here m is the number of edges in the graph. We observe that the Ω(m1/2 − &epsis;)-hardness of approximation applies to sparse graphs, and hence when expressed as a function of n, that is, the number of vertices, only an Ω(n1/2− &epsis;)-hardness follows. On the other hand, O(&sqrt;m)-approximation algorithms do not guarantee a sublinear (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 flow-based LP relaxation: an Ω(&sqrt;n) lower bound and O(&sqrt;m) upper bound. Motivated by this discrepancy in the upper and lower bounds, we study algorithms for EDP in directed and undirected graphs and obtain improved approximation ratios. We show that the greedy algorithm has an approximation ratio of O(min(n2/3, &sqrt;m)) in undirected graphs and a ratio of O(min(n4/5, &sqrt;m)) in directed graphs. For acyclic graphs we give an O(&sqrt;n ln n) approximation via LP rounding. These are the first sublinear approximation ratios for EDP. The results also extend to EDP with weights and to the uniform-capacity unsplittable flow problem (UCUFP).