English

Recognizing Union-Find trees is NP-complete

Computational Complexity 2017-01-06 v2 Data Structures and Algorithms

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\NP-complete.

Keywords

Cite

@article{arxiv.1510.07462,
  title  = {Recognizing Union-Find trees is NP-complete},
  author = {Kitti Gelle and Szabolcs Ivan},
  journal= {arXiv preprint arXiv:1510.07462},
  year   = {2017}
}
R2 v1 2026-06-22T11:28:53.187Z