|[+] Dynamic graphs: Euler tour trees, decremental connectivity in trees in O(1), fully dynamic connectivity in O(lg2 n), survey|
This lecture continues our theme of dynamic graphs. Beyond surveying results for several such problems, we'll focus on dynamic connectivity, where you can insert and/or delete edges, and the query is to determine whether two vertices are in the same connected component (i.e., have a path between them). We'll cover a few different results for this problem:
This will be our culmination of data structures for dynamic graphs; the next (final) lecture is about matching lower bounds.
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