Disjoint-set data structure: Difference between revisions

Revision as of 21:31, 11 December 2024

Revision as of 21:32, 11 December 2024

Line 17:

While there are several ways of implementing disjoint-set data structures, in practice they are often identified with a particular implementation known as a '''disjoint-set forest'''. This specialized type of [[Forest (graph theory)|forest]] performs union and find operations in near-constant [[Amortized analysis|amortized time]]. For a sequence of {{mvar|m}} addition, union, or find operations on a disjoint-set forest with {{mvar|n}} nodes, the total time required is {{math|[[Big O notation|''O'']](''m''α(''n''))}}, where {{math|α(''n'')}} is the extremely slow-growing [[inverse Ackermann function]]. Although disjoint-set forests do not guarantee this time per operation, each operation rebalances the structure so that subsequent operations become faster. As a result, disjoint-set forests are both [[asymptotically optimal]] and practically efficient.

Disjoint-set data structures play a key role in [[Kruskal's algorithm]] for finding the [[minimum spanning tree]] of a graph. The importance of minimum spanning trees means that disjoint-set data structures underliesupport a wide variety of algorithms. In addition, disjoint-setthese data structures also havefind applications toin symbolic computation, as well asand in compilers, especially for [[register allocation]] problems.

== History ==