Recognizing Union-Find trees is NP-complete

Kitti Gelle; Szabolcs Ivan

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arXiv · 1510.07462

Recognizing Union-Find trees is NP-complete

Kitti Gelle·Szabolcs Ivan

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Abstract

Disjoint-Set forests, consisting of Union-Find trees are data structures having a widespread practical application due to their efficiency. Despite them being well-known, no exact structural characterization of these trees is known (such a characterization exists for Union trees which are constructed without using path compression). In this paper we provide such a characterization and show that the decision problem whether a given tree is a Union-Find tree is $\NP$-complete.

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Kitti Gelle, Szabolcs Ivan. 2017-01-05. Recognizing Union-Find trees is NP-complete. https://arxiv.org/abs/1510.07462

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