Fully Dynamic Algorithm for the Steiner Tree Problem in Planar Graphs - Raikwar, Hemraj; Karmakar, Sushanta (International Symposium on Computing and Networking Workshops (Online), 2022)
In this paper, we propose a fully dynamic algorithm for the Steiner tree problem in a planar graph. We consider an undirected weighted planar graph G=(V, E) with positive real edge weights and a sequence of updates comprising of edge insertions and deletions. The goal is to maintain a Steiner tree (on the terminals) which is a good approximation of the minimum Steiner tree of the updated graph. We show that the proposed fully dynamic algorithm maintains a (2+ε) approximate Steiner tree in \tilde{O}(\vert S\vert ^{2}\sqrt{n}+\vert S\vert D+n) worst case update time where the symbols have usual meanings. The update time reduces to O(n(ε^{′})^{-2}) in a special case.