Decremental single-source reachability in planar digraphs
Giuseppe Francesco Italiano, Adam Karczmarz, Jakub Łącki, Piotr Sankowski · 2017
In this paper we show a new algorithm for the decremental single-source reachability problem in directed planar graphs. It processes any sequence of edge deletions in O(nlog2nloglogn) total time and explicitly maintains the set of vertices reachable from a fixed source vertex. Hence, if all edges are eventually deleted, the amortized time of processing each edge deletion is only O(log2 n loglogn), which improves upon a previously known O(√n) solution. We also show an algorithm for decremental maintenance of strongly connected components in directed planar graphs with the same total update time. These results constitute the first almost optimal (up to polylogarithmic factors) algorithms for both problems.