We give offline algorithms for processing a sequence of 2- and 3-edge and vertex connectivity queries in a fully-dynamic undirected graph. While the current best fully-dynamic online data structures for 3-edge and 3-vertex connectivity require O(n2/3) and O(n) time per update, respectively, our per-operation cost is only O(log n), optimal due to the dynamic connectivity lower bound of Patrascu and Demaine. Our approach utilizes a divide and conquer scheme that transforms a graph into smaller equivalents that preserve connectivity information. This construction of equivalents is closely-related to the development of vertex sparsifiers, and shares important connections to several upcoming results in dynamic graph data structures, including online models.
CITATION STYLE
Peng, R., Sandlund, B., & Sleator, D. D. (2019). Optimal offline dynamic 2, 3-Edge/Vertex connectivity. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 11646 LNCS, pp. 553–565). Springer Verlag. https://doi.org/10.1007/978-3-030-24766-9_40
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