Improving Time Bounds on Maximum Generalised Flow Computations by Contracting the Network
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
Second-Order Methods for Distributed Approximate Single- and Multicommodity Flow
RANDOM '98 Proceedings of the Second International Workshop on Randomization and Approximation Techniques in Computer Science
Dynamic programming and fast matrix multiplication
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Faster approximate lossy generalized flow via interior point algorithms
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Approximation results for flow shop scheduling problems with machine availability constraints
Computers and Operations Research
Homology flows, cohomology cuts
Proceedings of the forty-first annual ACM symposium on Theory of computing
Minimum cuts and shortest homologous cycles
Proceedings of the twenty-fifth annual symposium on Computational geometry
Scheduling unrelated parallel machines computational results
WEA'06 Proceedings of the 5th international conference on Experimental Algorithms
A faster combinatorial approximation algorithm for scheduling unrelated parallel machines
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Faster approximate multicommodity flow using quadratically coupled flows
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Operations Research Letters
On d-regular schematization of embedded paths
Computational Geometry: Theory and Applications
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The author presents an algorithm for solving linear programming problems that requires O((m+n)/sup 1.5/nL) arithmetic operations in the worst case, where m is the number of constraints, n the number of variables, and L a parameter defined in the paper. This result improves on the best known time complexity for linear programming by about square root n. A key ingredient in obtaining the speedup is a proper combination and balancing of precomputation of certain matrices by fast matrix multiplication and low-rank incremental updating of inverses of other matrices. Specializing the algorithm to problems such as minimum-cost flow, flow with losses and gains, and multicommodity flow leads to algorithms whose time complexity closely matches or is better than the time complexity of the best known algorithms for these problems.