Simplified Data Structure Lower Bounds for Dynamic Graph Connectivity
نویسنده
چکیده
The problem of dynamic connectivity in graphs has been extensively studied in the cell probe model. The task is to design a data structure that supports addition of edges and checks connectivity between arbitrary pair of vertices. Let w, tq, tu denote the word size, expected query time and worst case update time of a data structure for connectivity on graphs of size n. We provide simplified proofs of the following results: • Any data structure for connectivity with error at most 1 32 must have tq ≥ Ω ( logn logwtu ) . This was proved in the landmark paper of Fredman and Saks [FS89]. • For every δ > 0 and data structure for connectivity that makes no errors, if tu = o ( logn log logn ) , then tq ≥ Ω ( δn1−2δ ) . This was proved by Patrascu and Thorrup in [PT11].
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