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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. In FOCS 2016 (pp. 396-405). Piscataway, NJ: IEEE. doi:10.1109/FOCS.2016.44.

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 Creators:
Abraham, Ittai1, Author
Durfee, David1, Author
Koutis, Ioannis1, Author
Krinninger, Sebastian2, Author           
Peng, Richard1, Author
Affiliations:
1External Organizations, ou_persistent22              
2Algorithms and Complexity, MPI for Informatics, Max Planck Society, ou_24019              

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Free keywords: Computer Science, Data Structures and Algorithms, cs.DS
 Abstract: 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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Language(s): eng - English
 Dates: 20162016
 Publication Status: Issued
 Pages: 67 p.
 Publishing info: -
 Table of Contents: -
 Rev. Type: -
 Identifiers: DOI: 10.1109/FOCS.2016.44
BibTex Citekey: Abrahamdkkp2016
 Degree: -

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Title: 57th Annual IEEE Symposium on Foundations of Computer Science
Place of Event: New Brunswick, NJ, USA
Start-/End Date: 2016-10-09 - 2016-10-11

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Title: FOCS 2016
  Subtitle : 57th Annual IEEE Symposium on Foundations of Computer Science ; 9–11 October 2016 New Brunswick, New Jersey, USA
Source Genre: Proceedings
 Creator(s):
Affiliations:
Publ. Info: Piscataway, NJ : IEEE
Pages: - Volume / Issue: - Sequence Number: - Start / End Page: 396 - 405 Identifier: ISBN: 978-1-5090-3933-3