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  Fully Dynamic Spanners with Worst-Case Update Time

Bodwin, G., & Krinninger, S. (2016). Fully Dynamic Spanners with Worst-Case Update Time. Retrieved from http://arxiv.org/abs/1606.07864.

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1606.07864.pdf (Preprint), 528KB
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File downloaded from arXiv at 2017-01-31 14:08 To be presented at the European Symposium on Algorithms (ESA) 2016
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 Creators:
Bodwin, Greg1, Author
Krinninger, Sebastian2, 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: An $\alpha$-spanner of a graph $ G $ is a subgraph $ H $ such that $ H $ preserves all distances of $ G $ within a factor of $ \alpha $. In this paper, we give fully dynamic algorithms for maintaining a spanner $ H $ of a graph $ G $ undergoing edge insertions and deletions with worst-case guarantees on the running time after each update. In particular, our algorithms maintain: (1) a $3$-spanner with $ \tilde O (n^{1+1/2}) $ edges with worst-case update time $ \tilde O (n^{3/4}) $, or (2) a $5$-spanner with $ \tilde O (n^{1+1/3}) $ edges with worst-case update time $ \tilde O (n^{5/9}) $. These size/stretch tradeoffs are best possible (up to logarithmic factors). They can be extended to the weighted setting at very minor cost. Our algorithms are randomized and correct with high probability against an oblivious adversary. We also further extend our techniques to construct a $5$-spanner with suboptimal size/stretch tradeoff, but improved worst-case update time. To the best of our knowledge, these are the first dynamic spanner algorithms with sublinear worst-case update time guarantees. Since it is known how to maintain a spanner using small amortized but large worst-case update time [Baswana et al. SODA'08], obtaining algorithms with strong worst-case bounds, as presented in this paper, seems to be the next natural step for this problem.

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Language(s): eng - English
 Dates: 2016-06-242016-06-252016
 Publication Status: Published online
 Pages: 22 p.
 Publishing info: -
 Table of Contents: -
 Rev. Type: -
 Identifiers: arXiv: 1606.07864
URI: http://arxiv.org/abs/1606.07864
BibTex Citekey: BodwinK2016
 Degree: -

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