J ul 2 01 9 Near-Optimal Fully Dynamic Densest Subgraph

We give the first fully dynamic algorithm which maintains a (1 + ǫ)-approximate densest subgraph in worst-case time poly(logn, ǫ) per update with high probability. Dense subgraph discovery is an important primitive for many real-world applications such as community detection, link spam detection, distance query indexing, and computational biology. Our result improves upon the previous best approximation factor of (4+ǫ) for fully dynamic densest subgraph obtained by [Bhattacharya-Henzinger-Nanongkai-Tsourakakis, STOC‘15]. Our algorithm combines the uniform sparsification technique used in [Mitzenmacher-Pachocki-Peng-TsourakakisXu, KDD‘15] and [McGregor-Tench-Vorotnikova-Vu, MFCS‘15] along with an augmenting pathlike dual adjustment technique to maintain an approximate solution efficiently.