In a union step, a node p's set of descendants changes (in fact, becomes larger) if and only if it is the new root. Hence, for any step that keeps p as a root, p cannot be an interior node of a find-path, and thus its set of descendants either stays the same or becomes larger.
Aug 17, 2023
Aug 17, 2023 · Abstract:We analyze union-find using potential functions motivated by continuous algorithms, and give alternate proofs of the O(\log\log{n}) ...
We analyze union-find using potential functions motivated by continuous algorithms, and give alternate proofs of the $O(\log\log{n})$, $O(\log^{*}n)$, ...
Sep 13, 2024 · This paper carries out a potential function based amortized analysis of the running times of disjoint set union--find algorithms that reduce ...
Aug 25, 2023 · Bibliographic details on Simpler Analyses of Union-Find.
Union-Find is a powerful and efficient data structure that plays a crucial role in solving various graph-related problems and connectivity issues.
Feb 15, 2023 · Image Segmentation: Union-find can be used for identifying connected regions in an image. 3. Social Network Analysis: Union-find can be used ...
Our first data structure is a simple one with a very cute analysis. The ... It turns out there's a nice data structure called the Union-Find' data structure for ...
Jul 19, 2014 · By repeatedly taking the union of the root of the binomial tree to point to a singleton and doing a find on the deepest node, we perform an ...
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Mar 28, 2008 · I was thinking of using a union-find at work, but that nasty inverse-ackermann factor made it pretty much not feasible.