Dynamic Connectivity for Unit Disk Graphs ∗
نویسندگان
چکیده
Let S ⊂ R be a set of point sites. The unit disk graph UD(S) of S has vertex set S and an edge between two sites s, t if and only if |st| ≤ 1. We present a data structure that maintains the connected components of UD(S) when S changes dynamically. It takes O(log n) time to insert or delete a site in S and O(log n/ log log n) time to determine if two sites are in the same connected component. Here, n is the maximum size of S at any time. A simple variant improves the update time to O(log n log log n) at the cost of a slightly increased query time of O(log n).
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