The DOI matches its Crossref record; 39 of the 39 references it cites were found in a registry or an index.
A Fast Parametric Maximum Flow Algorithm and Applications
Abstract
The classical maximum flow problem sometimes occurs in settings in which the arc capacities are not fixed but are functions of a single parameter, and the goal is to find the value of the parameter such that the corresponding maximum flow or minimum cut satisfies some side condition. Finding the desired parameter value requires solving a sequence of related maximum flow problems. In this paper it is shown that the recent maximum flow algorithm of Goldberg and Tarjan can be extended to solve an important class of such parametric maximum flow problems, at the cost of only a constant factor in its worst-case time bound. Faster algorithms for a variety of combinatorial optimization problems follow from the result.
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Cites
Combinatorial optimization: networks and matroids
Lawler, E. L. (2021) · Cited by 3,359
On Nonlinear Fractional Programming
Dinkelbach, W. (1967) · Management Science · doi:10.1287/mnsc.13.7.492 · Cited by 3,139
Data Structures and Network Algorithms
Tarjan, R. E. (1983) · Society for Industrial and Applied Mathematics eBooks · doi:10.1137/1.9781611970265 · Cited by 2,057
Self-citationA new approach to the maximum-flow problem
Goldberg, A. V., & Tarjan, R. E. (1988) · Journal of the ACM · doi:10.1145/48014.61051 · Cited by 1,882
Self-citationSelf-adjusting binary search trees
Sleator, D. D., & Tarjan, R. E. (1985) · Journal of the ACM · doi:10.1145/3828.3835 · Cited by 1,228
Self-citationA data structure for dynamic trees
Sleator, D. D., & Tarjan, R. E. (1983) · Journal of Computer and System Sciences · doi:10.1016/0022-0000(83)90006-5 · Cited by 1,018
Self-citationCombinatorial Optimization with Rational Objective Functions
Megiddo, N. (1979) · Mathematics of Operations Research · doi:10.1287/moor.4.4.414 · Cited by 473
Decomposition of Finite Graphs Into Forests
Nash‐Williams, C. S. J. A. (1964) · Journal of the London Mathematical Society · doi:10.1112/jlms/s1-39.1.12 · Cited by 459
Minimum partition of a matroid into independent subsets
Edmonds, J. (1965) · Journal of Research of the National Bureau of Standards Section B Mathematics and Mathematical Physics · doi:10.6028/jres.069b.004 · Cited by 444
Algorithm for solution of a problem of maximum flow in networks with power estimation
Dinic, E. A. (1970) · Medical Entomology and Zoology · Cited by 389
Research works printed but not linked: 6
- R. K. Ahuja, J. B. Orlin, A fast and simple algorithm for the maximum flow problem, Working Paper, 1905-87, Sloan School of Management, Massachusetts Institute of Technology, Cambridge, MA, 1987
- Dinic E. A., 1970, Dokl. Akad. Nauk SSSR, 194, 754
- Ford, Jr. L. R., 1962, Flows in networks
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Cited by
Reachability and Distance Queries via 2-Hop Labels
Cohen, E., Halperin, E., Kaplan, H., & Zwick, U. (2003) · SIAM Journal on Computing · doi:10.1137/s0097539702403098 · Cited by 518
Metadata
- Authors
- Gallo, G., Grigoriadis, M. D., & Tarjan, R. E.
- Venue
- SIAM Journal on Computing
- Published
- 1989-02
- Volume
- 18
- Issue
- 1
- Pages
- 30-55
- ISSN
- 0097-5397
- 1095-7111
- Cited by
- 427
- References
- 39
- Language
- en
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