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Title: Fully dynamic all-pairs shortest paths with worst-case update-time revisited Sebastian Krinninger Max-Planck-Institut für Informatik - D1 AG1 Mittagsseminar (own work) D1, D2, D3, D4, D5, RG1, SWS, MMCIWe use this to send out email in the morning. AG Audience English
Date: Thursday, 15 December 2016 13:00 30 Minutes Saarbrücken E1 4 - MPI-INF 024
 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. Joint work with Ittai Abraham and Shiri Chechik To appear in SODA 2017 Preprint: https://arxiv.org/abs/1607.05132
Name(s): Sebastian Krinninger