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 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 NP-complete, complementing our earlier similar result for the union-by-size strategy.
Keywords
Cite
@article{arxiv.1704.07254,
title = {Recognizing Union-Find trees built up using union-by-rank strategy is NP-complete},
author = {Kitti Gelle and Szabolcs Ivan},
journal= {arXiv preprint arXiv:1704.07254},
year = {2017}
}
Comments
Accepted at 19th International Conference on Descriptional Complexity of Formal Systems, DCFS 2017