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Recognizing Union-Find Trees Built Up Using Union-By-Rank Strategy is NP-Complete

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) for the case assuming union-by-rank strategy for merging. In this paper we provide such a characterization by means of a simple $\textbf{PUSH}$ operation and show that the decision problem whether a given tree (along with the rank info of its nodes) is a Union-Find tree is $\mathbf {NP}$-complete, complementing our earlier similar result for the union-by-size strategy.
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https://hal.inria.fr/hal-01657003
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Submitted on : Wednesday, December 6, 2017 - 11:43:56 AM
Last modification on : Wednesday, December 6, 2017 - 2:24:59 PM

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Kitti Gelle, Szabolcs Iván. Recognizing Union-Find Trees Built Up Using Union-By-Rank Strategy is NP-Complete. 19th International Conference on Descriptional Complexity of Formal Systems (DCFS), Jul 2017, Milano, Italy. pp.152-163, ⟨10.1007/978-3-319-60252-3_12⟩. ⟨hal-01657003⟩

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