The maximum concurrent flow problem
Journal of the ACM (JACM)
Fast approximation algorithms for multicommodity flow problems
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
Fast approximation algorithms for fractional packing and covering problems
Mathematics of Operations Research
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
Approximate minimum-cost multicommodity flows in O˜(&egr;-2KNM) time
Mathematical Programming: Series A and B
Fast deterministic approximation for the multicommodity flow problem
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
Approximating Fractional Multicommodity Flow Independent of the Number of Commodities
SIAM Journal on Discrete Mathematics
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
Faster and simpler approximation algorithms for mixed packing and covering problems
Theoretical Computer Science
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Proceedings of the forty-second ACM symposium on Theory of computing
IPCO'05 Proceedings of the 11th international conference on Integer Programming and Combinatorial Optimization
IPCO'05 Proceedings of the 11th international conference on Integer Programming and Combinatorial Optimization
Feasible and accurate algorithms for covering semidefinite programs
SWAT'10 Proceedings of the 12th Scandinavian conference on Algorithm Theory
An approximation algorithm for the general mixed packing and covering problem
ESCAPE'07 Proceedings of the First international conference on Combinatorics, Algorithms, Probabilistic and Experimental Methodologies
A new approach to computing maximum flows using electrical flows
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
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We adapt a method proposed by Nesterov [16] to design an algorithm that computes ε-optimal solutions to fractional packing problems by solving O*(ε-1 √Kn) separable convex quadratic programs, where K is the maximum number of non-zeros per row and n is the number of variables. We also show that the quadratic program can be approximated to any degree of accuracy by an appropriately defined piecewise-linear program. For the special case of the maximum concurrent flow problem on a graph G =(V,E) with rational capacities and demands we obtain an algorithm that computes an Ε-optimal flow by solving O*(ε-1 K3/2|E| √|V| (log 1/ε+ LU + LD)) shortest path problems, where K is the number of commodities, and LU, LD are, respectively, the number of bits needed to store the capacities and demands. We also show that the complexity of computing a maximum multicommodity flow is O*(1/εlog2(1/ε)). In contrast, previous algorithms required Ω(ε-2) iterations.