Dynamic low-stretch spanning trees in subpolynomial time

Low-stretch spanning tree has been an important graph-theoretic object, as it is one of the building blocks for fast algorithms that solve symmetrically diagonally dominant linear systems, and a significant line of research has been devoted to finding constructions with optimal average stretch. In a very recent work by Goranci and Forster [STOC 2019], the authors initiated the study of low-stretch spanning trees in the dynamic setting, and they proposed a dynamic algorithm that maintains a spanning tree in n^{12 +}o⁽¹⁾ amortized update time with subpolynomial stretch in an unweighted graph on n vertices undergoing edge insertions and deletions demanded by an oblivious adversary. Our main results are twofold. First, we substantially improve the update time of Goranci and Forster [STOC 2019] from n^{12 +}o⁽¹⁾ to a subpolynomial of n^o(1). Second, we generalize our result to weighted graphs under the decremental setting. As far as we know, this is the first non trivial dynamic algorithm for maintaining low-stretch spanning tree for weighted graphs.