A Simple Optimal Solution for the Temporal Precedence Problem on Pure Pointer Machines

  • Authors:

  • Enrico Pontelli;Desh Ranjan

  • Affiliations:

  • Department of Computer Science, New Mexico State University, Las Cruces, NM 88003, USA;Department of Computer Science, New Mexico State University, Las Cruces, NM 88003, USA

  • Venue:
  • Theory of Computing Systems
  • Year:
  • 2005

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Abstract

In this paper we propose an optimal solution to the Temporal Precedence problem—i.e., the problem of managing the dynamic insertion of elements in a collection and the ability to determine, given two elements, which one has been inserted first. The problem is studied on pure pointer machines, i.e., pointer machines with no arithmetic capabilities. We provide an optimal solution (i.e., O(lg lg n) worst case time per operation, if n is the number of insertions) for this problem that is considerably simpler than the solutions previously presented in the literature. We also show how the solution can be improved to allow worst case O(1) insertions and linear space complexity.