On Tue, Feb 4, 2014 at 5:22 PM, Jeremy Harris <j...@wizmail.org> wrote:
> The attached patch replaces the existing siftup method for heapify with
> a siftdown method. Tested with random integers it does 18% fewer
> compares and takes 10% less time for the heapify, over the work_mem
> range 1024 to 1048576.
> Both algorithms appear to be O(n) (contradicting Wikipedia's claim
> that a siftup heapify is O(n log n)).

I think Wikipedia is right.  Inserting an a tuple into a heap is O(lg
n); doing that n times is therefore O(n lg n).  Your patch likewise
implements an outer loop which runs O(n) times and an inner loop which
runs at most O(lg n) times, so a naive analysis of that algorithm also
comes out to O(n lg n).  Wikipedia's article on
http://en.wikipedia.org/wiki/Heapsort explains why a tighter bound is
possible for the siftdown case.

I think I tested something like this at some point and concluded that
it didn't really help much, because building the initial heap was a
pretty small part of the runtime of a large sort.  It may still be
worth doing, though.

Robert Haas
EnterpriseDB: http://www.enterprisedb.com
The Enterprise PostgreSQL Company

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