#5470. Single-source shortest paths and strong connectivity in dynamic planar graphs

August 2026publication date
Proposal available till 19-05-2025
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Journal’s subject area:
Applied Mathematics;
Computational Theory and Mathematics;
Theoretical Computer Science;
Computer Networks and Communications;
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Abstract:
We give a fully dynamic single-source shortest paths data structure for planar weighted digraphs with O?(n4/5) worst-case update time and O(log2?n) query time. Here, a single update can either change the graph by inserting or deleting an edge, or reset the source s of interest. All known non-trivial planarity-exploiting exact dynamic single-source shortest paths algorithms to date had polynomial query time. We then extend our approach, obtaining a data structure that can maintain a planar digraph under edge insertions and deletions, and is capable of returning the identifier of the strongly connected component of any query vertex. The worst-case update and query time bounds are the same as for our single-source distance oracle. To the best of our knowledge, this is the first fully dynamic strong-connectivity algorithm achieving both sublinear update time and polylogarithmic query time for an important class of digraphs.
Keywords:
Dynamic graph algorithms; Planar graphs; Single-source shortest paths; Strong connectivity

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