@online{Krinningerarxiv16,
TITLE = {Fully Dynamic All-pairs Shortest Paths with Worst-case Update-time revisited},
AUTHOR = {Abraham, Ittai and Chechik, Shiri and Krinninger, Sebastian},
LANGUAGE = {eng},
URL = {http://arxiv.org/abs/1607.05132},
EPRINT = {1607.05132},
EPRINTTYPE = {arXiv},
YEAR = {2016},
MARGINALMARK = {$\bullet$},
ABSTRACT = {We revisit the classic problem of dynamically maintaining shortest paths between all pairs of nodes of a directed weighted graph. The allowed updates are insertions and deletions of nodes and their incident edges. We give worst-case guarantees on the time needed to process a single update (in contrast to related results, the update time is not amortized over a sequence of updates). Our main result is a simple randomized algorithm that for any parameter $c>1$ has a worst-case update time of $O(cn^{2+2/3} \log^{4/3}{n})$ and answers distance queries correctly with probability $1-1/n^c$, against an adaptive online adversary if the graph contains no negative cycle. The best deterministic algorithm is by Thorup [STOC 2005] with a worst-case update time of $\tilde O(n^{2+3/4})$ and assumes non-negative weights. This is the first improvement for this problem for more than a decade. Conceptually, our algorithm shows that randomization along with a more direct approach can provide better bounds.},
}