Worst-case analysis of set union algorithms. (English) Zbl 0632.68043

Tarjan, Robert E.; van Leeuwen, Jan

J. Assoc. Comput. Mach. 31, 245-281 (1984).

This paper analyzes the asymptotic worst-case running time of a number of variants of the well-known method of path compression for maintaining a collection of disjoint sets under union. We show that two one-pass methods proposed by van Leeuwen and van der Weide are asymptotically optimal, whereas several other methods, including one proposed by Rem and advocated by Dijkstra, are slower than the best methods.

MSC:

68Q25	Analysis of algorithms and problem complexity
68R99	Discrete mathematics in relation to computer science
68R10	Graph theory (including graph drawing) in computer science

Keywords:

equivalence algorithm; set union; inverse Ackermann function; asymptotic worst-case running time; path compression