Fully Dynamic Connectivity Oracles under General Vertex Updates

Author Kengo Nakamura

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Kengo Nakamura

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Kengo Nakamura. Fully Dynamic Connectivity Oracles under General Vertex Updates. In 28th International Symposium on Algorithms and Computation (ISAAC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 92, pp. 59:1-59:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)


We study the following dynamic graph problem: given an undirected graph G, we maintain a connectivity oracle between any two vertices in G under any on-line sequence of vertex deletions and insertions with incident edges. We propose two algorithms for this problem: an amortized update time deterministic one and a worst case update time Monte Carlo one. Both of them allow an arbitrary number of new vertices to insert. The update time complexity of the former algorithm is no worse than the existing algorithms, which allow only limited number of vertices to insert. Moreover, for relatively dense graphs, we can expect that the update time bound of the former algorithm meets a lower bound, and that of the latter algorithm can be seen as a substantial improvement of the existing result by introducing randomization.
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