Incremental exact min-cut in poly-logarithmic amortized update time
Goranci G, Henzinger MH, Thorup M. 2016. Incremental exact min-cut in poly-logarithmic amortized update time. 24th Annual European Symposium on Algorithms. ESA: Annual European Symposium on Algorithms, LIPIcs, vol. 57, 46.
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https://doi.org/10.4230/LIPIcs.ESA.2016.46
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Conference Paper
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Author
Goranci, Gramoz;
Henzinger, MonikaISTA ;
Thorup, Mikkel
Series Title
LIPIcs
Abstract
We present a deterministic incremental algorithm for exactly maintaining the size of a minimum cut with ~O(1) amortized time per edge insertion and O(1) query time. This result partially answers an open question posed by Thorup [Combinatorica 2007]. It also stays in sharp contrast to a polynomial conditional lower-bound for the fully-dynamic weighted minimum cut problem. Our algorithm is obtained by combining a recent sparsification technique of Kawarabayashi and Thorup [STOC 2015] and an exact incremental algorithm of Henzinger [J. of Algorithm 1997].
We also study space-efficient incremental algorithms for the minimum cut problem. Concretely, we show that there exists an O(n log n/epsilon^2) space Monte-Carlo algorithm that can process a stream of edge insertions starting from an empty graph, and with high probability, the algorithm maintains a (1+epsilon)-approximation to the minimum cut. The algorithm has ~O(1) amortized update-time and constant query-time.
Publishing Year
Date Published
2016-08-18
Proceedings Title
24th Annual European Symposium on Algorithms
Publisher
Schloss Dagstuhl - Leibniz-Zentrum für Informatik
Volume
57
Article Number
46
Conference
ESA: Annual European Symposium on Algorithms
Conference Location
Aarhus, Denmark
Conference Date
2016-08-22 – 2016-08-24
ISBN
ISSN
IST-REx-ID
Cite this
Goranci G, Henzinger MH, Thorup M. Incremental exact min-cut in poly-logarithmic amortized update time. In: 24th Annual European Symposium on Algorithms. Vol 57. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2016. doi:10.4230/LIPICS.ESA.2016.46
Goranci, G., Henzinger, M. H., & Thorup, M. (2016). Incremental exact min-cut in poly-logarithmic amortized update time. In 24th Annual European Symposium on Algorithms (Vol. 57). Aarhus, Denmark: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPICS.ESA.2016.46
Goranci, Gramoz, Monika H Henzinger, and Mikkel Thorup. “Incremental Exact Min-Cut in Poly-Logarithmic Amortized Update Time.” In 24th Annual European Symposium on Algorithms, Vol. 57. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2016. https://doi.org/10.4230/LIPICS.ESA.2016.46.
G. Goranci, M. H. Henzinger, and M. Thorup, “Incremental exact min-cut in poly-logarithmic amortized update time,” in 24th Annual European Symposium on Algorithms, Aarhus, Denmark, 2016, vol. 57.
Goranci G, Henzinger MH, Thorup M. 2016. Incremental exact min-cut in poly-logarithmic amortized update time. 24th Annual European Symposium on Algorithms. ESA: Annual European Symposium on Algorithms, LIPIcs, vol. 57, 46.
Goranci, Gramoz, et al. “Incremental Exact Min-Cut in Poly-Logarithmic Amortized Update Time.” 24th Annual European Symposium on Algorithms, vol. 57, 46, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2016, doi:10.4230/LIPICS.ESA.2016.46.
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arXiv 1611.06500