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  On Fully Dynamic Graph Sparsifiers

Abraham, I., Durfee, D., Koutis, I., Krinninger, S., & Peng, R. (2016). On Fully Dynamic Graph Sparsifiers. Retrieved from http://arxiv.org/abs/1604.02094.

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1604.02094.pdf (Preprint), 1019KB
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File downloaded from arXiv at 2017-01-31 14:13 A preliminary version of this paper appears in the 57th Annual IEEE Symposium on Foundations of Computer Science (FOCS 2016)
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 Urheber:
Abraham, Ittai1, Autor
Durfee, David1, Autor
Koutis, Ioannis1, Autor
Krinninger, Sebastian2, Autor           
Peng, Richard1, Autor
Affiliations:
1External Organizations, ou_persistent22              
2Algorithms and Complexity, MPI for Informatics, Max Planck Society, ou_24019              

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Schlagwörter: Computer Science, Data Structures and Algorithms, cs.DS
 Zusammenfassung: We initiate the study of dynamic algorithms for graph sparsification problems and obtain fully dynamic algorithms, allowing both edge insertions and edge deletions, that take polylogarithmic time after each update in the graph. Our three main results are as follows. First, we give a fully dynamic algorithm for maintaining a $ (1 \pm \epsilon) $-spectral sparsifier with amortized update time $poly(\log{n}, \epsilon^{-1})$. Second, we give a fully dynamic algorithm for maintaining a $ (1 \pm \epsilon) $-cut sparsifier with \emph{worst-case} update time $poly(\log{n}, \epsilon^{-1})$. Both sparsifiers have size $ n \cdot poly(\log{n}, \epsilon^{-1})$. Third, we apply our dynamic sparsifier algorithm to obtain a fully dynamic algorithm for maintaining a $(1 + \epsilon)$-approximation to the value of the maximum flow in an unweighted, undirected, bipartite graph with amortized update time $poly(\log{n}, \epsilon^{-1})$.

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Sprache(n): eng - English
 Datum: 2016-04-072016-10-072016
 Publikationsstatus: Online veröffentlicht
 Seiten: 67 p.
 Ort, Verlag, Ausgabe: -
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 Identifikatoren: arXiv: 1604.02094
URI: http://arxiv.org/abs/1604.02094
BibTex Citekey: Abrahamdkkp16
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