One of the best known methods for external sorting on tapes is the polyphase sort.
Principle: The basic strategy of this sort is to distribute ordered initial runs of predetermined size on the available tapes and then to repeatedly merge these runs in multiple phases in which each phase has a predetermined number of merges before a new target tape is selected.
To distribute the initial runs a Fibonacci distribution is adopted. After the distribution of the runs according to Fibonacci distribution, the merging procedure is continued until the tape with the least number of run lists is empty. When this occurs the remaining working tapes are logically rotated such that the newly emptied tape becomes the new target tape and the old target tape then becomes one of the working tapes to be merged. The sort ends when all runs are merged into one.
Let the number of tapes be T and p = T - 1. The Fibonacci distribution for p = 3 is given.
Level
s
Tape
Total number of runs
1
2
3
1
0
0
1
1
2
1
1
1
3
3
1
2
2
5
4
2
3
4
9
5
4
6
7
17
6
7
11
13
31
7
13
20
24
57
8
24
37
44
105
9
44
68
81
193
Algorithm:
1. Let A be the list of N unsorted elements and R be the number of runs.
2. Let T1, T2, T3 and T4 be the tapes on which sorting is done.
3. Split the list A into R=N runs so that each run has only one element.
4. If R is not equal to perfect Fibonacci distribution then add dummy records to bring up perfect Fibonacci distribution.
5. Distribute the records in the remaining tapes according to the Fibonacci distribution.
6. Merge 3 runs, one from each tape and put into next empty tape.
7. Repeat step 6 till a single run is generated.