The Temporal Precedence Problem

Abstract.

In this paper we analyze the complexity of the Temporal Precedence Problem on pointer machines. The problem is to support efficiently two operations: insert and precedes. The operation insert (a) introduces a new element a , while precedes (a,b) returns true iff element a was temporally inserted before element b . We provide a solution to the problem with worst-case time complexity O( lg lg n) per operation, where n is the number of elements inserted. We also demonstrate that the problem has a lower bound of Ω( lg lg n) on pointer machines. Thus the proposed scheme is optimal on pointer machines.