Dynamic Approximate All-Pairs Shortest Paths: Breaking the O(mn) Barrier and Derandomization

@article{Henzinger2013DynamicAA,
  title={Dynamic Approximate All-Pairs Shortest Paths: Breaking the O(mn) Barrier and Derandomization},
  author={Monika Henzinger and Sebastian Krinninger and Danupon Nanongkai},
  journal={2013 IEEE 54th Annual Symposium on Foundations of Computer Science},
  year={2013},
  pages={538-547}
}
We study dynamic (1 + ϵ)-approximation algorithms for the all-pairs shortest paths problem in unweighted undirected n-node m-edge graphs under edge deletions. The fastest algorithm for this problem is a randomized algorithm with a total update time of Ȏ(mn) and constant query time by Roditty and Zwick (FOCS 2004). The fastest deterministic algorithm is from a 1981 paper by Even and Shiloach (JACM 1981); it has a total update time of O(mn2) and constant query time. We improve these results as… 

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