Reducing the symmetric matrix eigenvalue problem to matrix multiplications
SIAM Journal on Scientific Computing
Iterative solution methods
Fast approximation algorithms for multicommodity flow problems
Selected papers of the 23rd annual ACM symposium on Theory of computing
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
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
A combinatorial, primal-dual approach to semidefinite programs
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Speeding-up linear programming using fast matrix multiplication
SFCS '89 Proceedings of the 30th Annual Symposium on Foundations of Computer Science
IEEE Transactions on Pattern Analysis and Machine Intelligence
Solving Elliptic Finite Element Systems in Near-Linear Time with Support Preconditioners
SIAM Journal on Numerical Analysis
Proceedings of the forty-second ACM symposium on Theory of computing
Approaching Optimality for Solving SDD Linear Systems
FOCS '10 Proceedings of the 2010 IEEE 51st Annual Symposium on Foundations of Computer Science
Electrical flows, laplacian systems, and faster approximation of maximum flow in undirected graphs
Proceedings of the forty-third annual ACM symposium on Theory of computing
Runtime guarantees for regression problems
Proceedings of the 4th conference on Innovations in Theoretical Computer Science
A simple, combinatorial algorithm for solving SDD systems in nearly-linear time
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
| Hi-index | 0.00 |
The maximum multicommodity flow problem is a natural generalization of the maximum flow problem to route multiple distinct flows. Obtaining a 1-ε approximation to the multicommodity flow problem on graphs is a well-studied problem. In this paper we present an adaptation of recent advances in single-commodity flow algorithms to this problem. As the underlying linear systems in the electrical problems of multicommodity flow problems are no longer Laplacians, our approach is tailored to generate specialized systems which can be preconditioned and solved efficiently using Laplacians. Given an undirected graph with m edges and k commodities, we give algorithms that find 1-ε approximate solutions to the maximum concurrent flow problem and maximum weighted multicommodity flow problem in time O(m4/3poly(k,ε-1)).