Computer Time for Address Calculation Sorting

ABSTRACT

For each item to be sorted by address calculation, a location in the file is determined by a linear formula. It is placed there if the location is empty. If there is an item at the specified location, a search is made to find the closest empty space to this spot. The item at the specified location, together with adjacent items, is moved by a process similar to musical chairs, so that the item to be filed can be entered in its proper order in the file. A generalized flowchart for computer address calculation sorting is presented here. A mathematical analysis using average expectation follows. Formulas are derived to determine the number of computer operations required. Further formulas are derived which determine the time required for an address calculation sort in terms of specific computer orders. Several examples are given. A sorting problem solved elsewhere in the literature by an empirical method is solved by the formulas developed here to demonstrate their practical application.

REFERENCES

• 1: E. J. Isaac , R. C. Singleton, Sorting by Address Calculation, Journal of the ACM (JACM), v.3 n.3, p.169-174, July 1956 [doi>10.1145/320831.320834]
• 2: Edward H. Friend, Sorting on Electronic Computer Systems, Journal of the ACM (JACM), v.3 n.3, p.134-168, July 1956 [doi>10.1145/320831.320833]

INDEX TERMS

Primary Classification:
  F. Theory of Computation
  F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY
      F.2.2 Nonnumerical Algorithms and Problems
          Subjects: Sorting and searching

Additional Classification:
  G. Mathematics of Computing
  G.2 DISCRETE MATHEMATICS

General Terms:
Measurement, Performance, Reliability, Theory