Report Number: CS-TR-77-603
Institution: Stanford University, Department of Computer Science
Title: Reference machines require non-linear time to maintain disjoint sets
Author: Tarjan, Robert Endre
Date: March 1977
Abstract: This paper describes a machine model intended to be useful in deriving realistic complexity bounds for tasks requiring list processing. As an example of the use of the model, the paper shows that any such machine requires non-linear time in the worst case to compute unions of disjoint sets on-line. All set union algorithms known to me are instances of the model and are thus subject to the derived bound. One of the known algorithms achieves the bound to within a constant factor.
http://i.stanford.edu/pub/cstr/reports/cs/tr/77/603/CS-TR-77-603.pdf