%0 Conference Proceedings
%T Recognizing Union-Find Trees Built Up Using Union-By-Rank Strategy is NP-Complete
%+ University of Szeged [Szeged]
%A Gelle, Kitti
%A Iván, Szabolcs
%Z Part 2: Contributed Papers
%< avec comité de lecture
%( Lecture Notes in Computer Science
%B 19th International Conference on Descriptional Complexity of Formal Systems (DCFS)
%C Milano, Italy
%Y Giovanni Pighizzini
%Y Cezar Câmpeanu
%I Springer International Publishing
%3 Descriptional Complexity of Formal Systems
%V LNCS-10316
%P 152-163
%8 2017-07-03
%D 2017
%R 10.1007/978-3-319-60252-3_12
%Z Computer Science [cs]Conference papers
%X 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.
%G English
%Z TC 1
%Z WG 1.2
%2 https://inria.hal.science/hal-01657003/document
%2 https://inria.hal.science/hal-01657003/file/440206_1_En_12_Chapter.pdf
%L hal-01657003
%U https://inria.hal.science/hal-01657003
%~ IFIP-LNCS
%~ IFIP
%~ IFIP-TC
%~ IFIP-TC1
%~ IFIP-WG
%~ IFIP-DCFS
%~ IFIP-WG1-2
%~ IFIP-LNCS-10316