Ordered dictionaries compared

[Dan Stromberg]

What kind of ordered dictionaries?  Sorted by key.

I've redone the previous comparison, this time with a better red-black tree implementation courtesy of Duncan G. Smith.

The comparison is at http://stromberg.dnsalias.org/~strombrg/python-tree-and-heap-comparison/just-trees/

The Red-Black tree gave a much better showing this time, but it gave just one 2nd place on one workload-interpreter - still kinda lackluster.  It took 1st place 0 times.

[Antoine Pitrou]

Dan Stromberg <drsalists <at> gmail.com> writes:
>
> What kind of ordered dictionaries?  Sorted by key.

Calling them "sorted dictionaries" avoids any confusions with Python's
standard OrderedDict class:
http://docs.python.org/3.3/library/collections.html#ordereddict-objects

Regards

Antoine.

[duncan smith]

A quick test of my Red Black Tree and Treap (Python 2.7).


>>> def test_trees(data, randomize=True):
cpy = data[:] # for deletion
if randomize:
random.shuffle(data)
random.shuffle(cpy)
t = binary_trees.RedBlackTree()
start = time.time()
for datum in data:
t.insert(datum)
print 'Red Black Tree insertion %s' % (time.time() - start)
start = time.time()
for datum in data:
t.find(datum)
print 'Red Black Tree find %s' % (time.time() - start)
start = time.time()
for datum in cpy:
t.delete(datum)
print 'Red Black Tree deletion %s' % (time.time() - start)
t = binary_trees.Treap()
start = time.time()
for datum in data:
t.insert(datum)
print
print 'Treap insertion %s' % (time.time() - start)
start = time.time()
for datum in data:
t.find(datum)
print 'Treap find %s' % (time.time() - start)
start = time.time()
for datum in cpy:
t.delete(datum)
print 'Treap deletion %s' % (time.time() - start)


>>> test_trees(range(100000))
Red Black Tree insertion 5.42807197571
Red Black Tree find 1.58799219131
Red Black Tree deletion 3.87580800056

Treap insertion 6.79647684097
Treap find 2.11693120003
Treap deletion 4.61243915558
>>>
>>> test_trees(range(100000), False)
Red Black Tree insertion 6.29647898674
Red Black Tree find 1.157143116
Red Black Tree deletion 2.74785804749

Treap insertion 3.87288999557
Treap find 1.48776102066
Treap deletion 1.88962197304
>>>


RBT is quicker than Treap for insertion with randomized data, but slower
with ordered data. Randomized data will tend to minimize the number of
tree rotations needed to keep the RBT balanced, whilst the Treap will be
performing rotations to maintain the heap property in an already
reasonably well balanced tree. With ordered data the RBT will have to
work harder to keep the tree balanced, whilst the Treap will be able to
maintain the heap property with fewer rotations.

No surprise that find() is generally quicker for RBTs, they tend to be
better balanced.

Deletion is a bit more confusing. I suppose deletion from a better
balanced tree will tend to be quicker, but deletion from a treap
constructed from ordered data is (for some reason) quickest of all.

All these operations require a call to find(), and that is generally
going to be quicker for RBTs. Treaps tend to require fewer subsequent
rotations, but they have variable worth (in terms of rebalancing).

Looks like RBTs are better than treaps if they are being populated with
randomly ordered data, but not if they are being populated with ordered
data. RBTs are better for use cases that are heavy on finds.

Both types of tree appear to be better balanced (on the basis of the
find results) if populated from ordered data. Treaps appear to perform
better on insertion, find and deletion when populated from ordered data.

Duncan

[Dan Stromberg]

On Thu, May 23, 2013 at 9:41 AM, duncan smith <buz...@invalid.invalid> wrote:

RBT is quicker than Treap for insertion with randomized data, but slower with ordered data. Randomized data will tend to minimize the number of tree rotations needed to keep the RBT balanced, whilst the Treap will be performing rotations to maintain the heap property in an already reasonably well balanced tree. With ordered data the RBT will have to work harder to keep the tree balanced, whilst the Treap will be able to maintain the heap property with fewer rotations.

No surprise that find() is generally quicker for RBTs, they tend to be better balanced.

Deletion is a bit more confusing. I suppose deletion from a better balanced tree will tend to be quicker, but deletion from a treap constructed from ordered data is (for some reason) quickest of all.

All these operations require a call to find(), and that is generally going to be quicker for RBTs. Treaps tend to require fewer subsequent rotations, but they have variable worth (in terms of rebalancing).

Looks like RBTs are better than treaps if they are being populated with randomly ordered data, but not if they are being populated with ordered data. RBTs are better for use cases that are heavy on finds.

Both types of tree appear to be better balanced (on the basis of the find results) if populated from ordered data. Treaps appear to perform better on insertion, find and deletion when populated from ordered data.

 

Strange.  I was comparing randomized data (95% get, 50-50 get and set, 95% set) when I found that treaps were quite a bit faster than red black trees.

The code I used is here: http://stromberg.dnsalias.org/svn/python-tree-and-heap-comparison/trunk/

See also https://en.wikipedia.org/wiki/Binary_search_tree#Performance_comparisons , which found that treaps were faster on average the red black trees.

[duncan smith]

Dan,
Faster on average, but it depends what you're averaging over. As
far as insertion and deletions are concerned my results agree with those
in the paper, except they have treaps performing slightly faster than
RBTs for insertion with randomly ordered data.

Deletion in your code is slightly different to that in mine. It might
make a difference. Also, your code doesn't use sentinels (pros and
cons). It could be down to implementation details.

Duncan