@inproceedings{11785,
  abstract     = {Recently we presented the first algorithm for maintaining the set of nodes reachable from a source node in a directed graph that is modified by edge deletions with 𝑜(𝑚𝑛) total update time, where 𝑚 is the number of edges and 𝑛 is the number of nodes in the graph [Henzinger et al. STOC 2014]. The algorithm is a combination of several different algorithms, each for a different 𝑚 vs. 𝑛 trade-off. For the case of 𝑚=Θ(𝑛1.5) the running time is 𝑂(𝑛2.47), just barely below 𝑚𝑛=Θ(𝑛2.5). In this paper we simplify the previous algorithm using new algorithmic ideas and achieve an improved running time of 𝑂̃ (min(𝑚7/6𝑛2/3,𝑚3/4𝑛5/4+𝑜(1),𝑚2/3𝑛4/3+𝑜(1)+𝑚3/7𝑛12/7+𝑜(1))). This gives, e.g., 𝑂(𝑛2.36) for the notorious case 𝑚=Θ(𝑛1.5). We obtain the same upper bounds for the problem of maintaining the strongly connected components of a directed graph undergoing edge deletions. Our algorithms are correct with high probabililty against an oblivious adversary.},
  author       = {Henzinger, Monika H and Krinninger, Sebastian and Nanongkai, Danupon},
  booktitle    = {42nd International Colloquium on Automata, Languages and Programming},
  isbn         = {9783662476710},
  issn         = {0302-9743},
  location     = {Kyoto, Japan},
  pages        = {725 -- 736},
  publisher    = {Springer Nature},
  title        = {{Improved algorithms for decremental single-source reachability on directed graphs}},
  doi          = {10.1007/978-3-662-47672-7_59},
  volume       = {9134},
  year         = {2015},
}