As to the complexity, (to me) it looks very much like O(n^2) in time.

I agree. the Perl version certainly looks to be tending that way with respect to the time for a number of records with the number of buffers fixed.

But the number of buffers also has a non-linear effect that is harder to quantify.

These are timings taking using the Perl prototype:

Array               N u m b e r   o f   b u f f e r s.
Size                2               4               8               16
+        
10000     9.710932970    14.441396952    16.980458975     17.980459929
20000    38.186435938    54.618164063    65.470575094     68.913941145
40000   148.056374073   224.696855068   244.073187113    260.217727184
80000   310.495392084   882.082360983   969.694694996   1098.488962889

[download]

But Perl's internal overheads tend to cloud the issue.

These are a similar set of timings, (though with 1000 times as many records), from a straight Perl to C conversion:

Array                 N u m b e r   o f   b u f f e r s.
Size                  2               4               8              1
+6
 10000000   0.248736811     0.497881829     0.799180768     1.33560723
+0
 20000000   0.285630879     1.024963784     1.879727758     3.58831668
+6
 40000000   0.402336371     1.211978628     3.943654854     7.76231127
+6
 80000000   0.966428312     2.093228984    10.674847289    15.20866750
+8
160000000   3.682530644     7.499381800    16.773807549    34.45496560
+7

[download]

That's a lot less pessimistic of the algorithm.

Based on the timings alone, it looks to be linear(ish) in the number of buffers and (um) log.quadratic in the number of records?

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In reply to Re^2: Can you improve upon my algorithm. by BrowserUk
in thread Can you improve upon my algorithm. by BrowserUk

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