English

# Item

ITEM ACTIONSEXPORT
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.

Item is

show hide
Genre: Paper

### Files

show Files
hide Files
:
1606.07864.pdf (Preprint), 528KB
Name:
1606.07864.pdf
Description:
File downloaded from arXiv at 2017-01-31 14:08 To be presented at the European Symposium on Algorithms (ESA) 2016
Visibility:
Public
MIME-Type / Checksum:
application/pdf / [MD5]
-
-

show

### Creators

show
hide
Creators:
Bodwin, Greg1, Author
Krinninger, Sebastian2, Author
Affiliations:
1External Organizations, ou_persistent22
2Algorithms and Complexity, MPI for Informatics, Max Planck Society, ou_24019

### Content

show
hide
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.

### Details

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

show

show

show

show