Recognizing Union-Find trees is NP-complete

October 26, 2015 · The Ethereal · 🏛 Information Processing Letters

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Authors Kitti Gelle, Szabolcs Ivan arXiv ID 1510.07462 Category cs.CC: Computational Complexity Cross-listed cs.DS Citations 3 Venue Information Processing Letters Last Checked 2 months ago
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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