A class of algorithms which require nonlinear time to maintain disjoint sets

摘要

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 defines a class of algorithms which compute unions of disjoint sets on-line, and proves that any such algorithm requires nonlinear time in the worst case. All set union algorithms known to the author 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.