Fully Dynamic Algorithm for the Steiner Tree Problem in Planar Graphs

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 (...

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Bibliographic Details
Published in:International Symposium on Computing and Networking Workshops (Online) pp. 416 - 420
Main Authors: Raikwar, Hemraj, Karmakar, Sushanta
Format: Conference Proceeding
Language:English
Published: IEEE 01.11.2022
Subjects:
Approximation algorithms
Conferences
dynamic distance oracle
fully dynamic algorithm
Heuristic algorithms
Steiner tree
Steiner trees
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ISSN:2832-1324
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Summary: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+\epsilon) 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(\epsilon^{\prime})^{-2}) in a special case.
ISSN:2832-1324
DOI:10.1109/CANDARW57323.2022.00064