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Recognizing Union-Find trees is NP-complete (1510.07462v2)
Published 26 Oct 2015 in cs.CC and cs.DS
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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