Fully dynamic all-pairs shortest paths with worst-case update-time revisited

Ittai Abraham, Shiri Chechik, Sebastian Krinninger
2017 Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms  
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
more » ... 2/3^4/3n) 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 Õ(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.
doi:10.1137/1.9781611974782.28 dblp:conf/soda/AbrahamCK17 fatcat:4qvphbqv6zfchjpywqht656h6y