The DOI matches its Crossref record; 22 of the 22 references it cites were found in a registry or an index.
Faster Scaling Algorithms for Network Problems
Abstract
This paper presents algorithms for the assignment problem, the transportation problem, and the minimum-cost flow problem of operations research. The algorithms find a minimum-cost solution, yet run in time close to the best-known bounds for the corresponding problems without costs. For example, the assignment problem (equivalently, minimum-cost matching in a bipartite graph) can be solved in $O(\sqrt {nm} \log (nN))$ time, where $n,m$, and N denote the number of vertices, number of edges, and largest magnitude of a cost; costs are assumed to be integral. The algorithms work by scaling. As in the work of Goldberg and Tarjan, in each scaled problem an approximate optimum solution is found, rather than an exact optimum.
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Cites
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The Hungarian method for the assignment problem
Kuhn, H. W. (1955) · Naval Research Logistics Quarterly · doi:10.1002/nav.3800020109 · Cited by 13,120
The Design and Analysis of Computer Algorithms
Aho, A. V., & Hopcroft, J. E. (1974) · CERN Document Server (European Organization for Nuclear Research) · Cited by 9,403
Combinatorial Optimization: Algorithms and Complexity.
Johnson, D. S., Papadimitriou, C. H., & Steiglitz, K. (1984) · The American Mathematical Monthly · doi:10.2307/2322374 · Cited by 5,942
Combinatorial optimization:Algorithms and complexity
Rabiner, L. (1984) · IEEE Transactions on Acoustics, Speech, and Signal Processing · doi:10.1109/tassp.1984.1164450 · Cited by 3,576
Combinatorial optimization: networks and matroids
Lawler, E. L. (2021) · Cited by 3,359
An $n^{5/2} $ Algorithm for Maximum Matchings in Bipartite Graphs
Hopcroft, J. E., & Karp, R. M. (1973) · SIAM Journal on Computing · doi:10.1137/0202019 · Cited by 2,802
Bellman, R. (1958) · Quarterly of Applied Mathematics · doi:10.1090/qam/102435 · Cited by 2,758
Fibonacci heaps and their uses in improved network optimization algorithms
Fredman, M. L., & Tarjan, R. E. (1987) · Journal of the ACM · doi:10.1145/28869.28874 · Cited by 2,656
Self-citationTheoretical Improvements in Algorithmic Efficiency for Network Flow Problems
Edmonds, J., & Karp, R. M. (1972) · Journal of the ACM · doi:10.1145/321694.321699 · Cited by 2,528
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CARLSSON, G., ZOMORODIAN, A., COLLINS, A., & GUIBAS, L. J. (2005) · International Journal of Shape Modeling · doi:10.1142/s0218654305000761 · Cited by 287
Persistence barcodes for shapes
Carlsson, G., Zomorodian, A., Collins, A., & Guibas, L. (2004) · Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing · doi:10.1145/1057432.1057449 · Cited by 133
Metadata
- Authors
- Gabow, H. N., & Tarjan, R. E.
- Venue
- SIAM Journal on Computing
- Published
- 1989-10
- Volume
- 18
- Issue
- 5
- Pages
- 1013-1036
- ISSN
- 0097-5397 (ISSN-L)
- 1095-7111
- OpenAlex
- W1969357318
- Cited by
- 414
- References
- 22
- FWCI
- 6.46
- Type
- journal article
- Language
- en
- Open access
- closed
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Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
