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I previously added code that took care of that case, where two nodes
needed to be merged that both have queues. However, I convinced
myself at the time, that the case would never happen. So, the code
probably needs to be thought-through a bit more with more testing,
but my hope is that merging the queues isn't necessary. I haven't
been able to crash the data structure without that case while using
many priorities, but it still requires investigation.<br>
<br>
On 11/10/2011 12:01 AM, Ulf Wiger wrote:
<blockquote
cite="mid:756EEC5C-E42B-435D-B343-2A41A5A91858@erlang-solutions.com"
type="cite">
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<div><br>
</div>
<div>Always nice when the simplest approaches prove to be among
the fastest. :)</div>
<div><br>
</div>
<div>You don't have a case for merging two trees where the roots
are the same and both are queues. I guess there isn't any
perfect way to merge the queues, unless you put timestamps on
each entry…</div>
<div><br>
</div>
<div>BR,</div>
<div>Ulf W</div>
<br>
<div>
<div>On 10 Nov 2011, at 08:45, Michael Truog wrote:</div>
<br>
<blockquote type="cite">
<div> I modified the example to extend it with queues and it
does compare very well, being slightly faster. I still
believe it needs to be tested more, but the implementation
becomes simpler and you don't need the static priority
limitations, which is nice. The link is:<br>
<a moz-do-not-send="true"
href="https://github.com/okeuday/pqueue/blob/master/src/pqueue2.erl">https://github.com/okeuday/pqueue/blob/master/src/pqueue2.erl</a><br>
<br>
with erlbench results here ((with R14B02, without HiPE) on
an AMD Phenom 9950 Quad-Core (64 bit) running Linux
2.6.32-23-generic (Ubuntu)):<br>
TEST run_priority_queue<br>
N == 1000000 (10 runs)<br>
pqueue get: 481774.3 µs ( 1.4), set:
525589.1 µs ( 1.0)<br>
pqueue2 get: 332711.2 µs ( 1.0), set:
680209.0 µs ( 1.3)<br>
priority_queue get: 362588.9 µs ( 1.1), set:
1443674.2 µs ( 2.7)<br>
<br>
<br>
On 11/09/2011 08:58 AM, Michael Truog wrote:
<blockquote cite="mid:4EBAB14E.2080805@gmail.com"
type="cite"> I think the skew heap I have needs some work,
because it seems to come only from Okasaki's code example,
so it doesn't take into consideration his
suggestions/exercises. So, only insert is O(1), and the
min would need to be stored separately to get O(1) instead
of O(log(N)). He had a suggestion for making the merge of
two heaps O(1), but I wasn't as concerned about that
operation. It seems hard to get an "out" operation that
is O(1) amortized, that is removing the min from the heap
(hopefully O(log(N)) worst case). I will look at testing
a heap implementation to see how it might work out.
Thanks for the information.<br>
<br>
On 11/09/2011 01:00 AM, Ulf Wiger wrote:
<blockquote
cite="mid:AD5ABC43-3687-40DD-972E-E6FFF69965F4@erlang-solutions.com"
type="cite">
<div><br>
</div>
<div>Yeah, obviously, mine was just a sketch, thrown
down as an executable comment and optimized for
brevity. :)</div>
<div><br>
</div>
<div>(Although I'm not convinced, from reading, that
Michael's implementation is faster than mine. Anyone
who cares deeply enough could of course measure. I am
currently not shopping for a faster priority queue, so
I will pass on that.)</div>
<div><br>
</div>
<div>As an aside, it was a simple skew heap exercise,
presented by Chris Okasaki, that made me invite Quviq
to Ericsson for the first Erlang QuickCheck pilots. </div>
<div><br>
</div>
<div>The task was to reverse-engineer the insertion
order of a particular skew heap. John Hughes solved it
with a "brute force approach", using QuickCheck to
test his assumptions. Watching him do exploratory
hacking with QuickCheck was so much fun that, once he
ported QuickCheck to Erlang, I had to try to find out
if it could be put to use in a commercial project.</div>
<div><br>
</div>
<div>Unfortunately - or fortunately - for Quviq, the
only candidate for a useful pilot was stateful, and
QuickCheck had no support for that. For lesser minds,
that might have been a problem, but John and Thomas
quickly invented the statem model. :)</div>
<div><br>
</div>
<div>BR,</div>
<div>Ulf W</div>
<div><br>
</div>
<div>On 9 Nov 2011, at 09:45, Zabrane Mickael wrote:</div>
<div><br>
<blockquote type="cite">
<div>Hi Ulf,
<div><br>
</div>
<div>Michael Truog already has a SkewBinHeap
impelmentation here:</div>
<div><a moz-do-not-send="true"
href="https://github.com/okeuday/skewbinheap">https://github.com/okeuday/skewbinheap</a></div>
<div><br>
</div>
<div>
<div>Regards,</div>
<div>Zabrane</div>
<div><br>
</div>
<div>
<div>On Nov 9, 2011, at 9:42 AM, Ulf Wiger
wrote:</div>
<br>
<blockquote type="cite">
<div>
<div>I'm partial to skew heaps, mainly
because they are so elegant.</div>
<div><br>
</div>
<div><a moz-do-not-send="true"
href="http://www.cse.yorku.ca/%7Eandy/courses/4101/lecture-notes/LN5.pdf">http://www.cse.yorku.ca/~andy/courses/4101/lecture-notes/LN5.pdf</a></div>
<div><br>
</div>
<div>Something like this (although I've
done only basic testing):</div>
<div><br>
</div>
<div>
<div>-module(skew).</div>
<div>-export([new/0, in/2, out/1]).</div>
<div><br>
</div>
<div>new() -></div>
<div> [].</div>
<div><br>
</div>
<div>in(X, Heap) -></div>
<div> merge({X,[],[]}, Heap).</div>
<div><br>
</div>
<div>out([]) -></div>
<div> error;</div>
<div>out({X, L, R}) -></div>
<div> {X, merge(L, R)}.</div>
<div><br>
</div>
<div>merge({P0,Pl,Pr}, {Q0,_,_} = Q)
when P0 < Q0 -></div>
<div> {P0, Pr, merge(Pl,Q)};</div>
<div>merge({P0,_,_} = P, {Q0,Ql,Qr})
when P0 > Q0 -></div>
<div> {Q0, Qr, merge(Ql,P)};</div>
<div>
<div>merge({P0,Pl,Pr} = P,{P0,Ql,Qr})
-> % equal roots</div>
<div> merge(P, merge(merge(Pl,Pr),
merge(Ql,Qr)));</div>
</div>
<div>merge([], Q) -> Q;</div>
<div>merge(P, []) -> P.</div>
</div>
<div><br>
</div>
<div>The cost is amortized O(log N) for
in/2 and out/1. For peeking at the min,
it's O(1).</div>
<div><br>
</div>
<div>BR,</div>
<div>Ulf W</div>
<br>
<div>
<div>On 9 Nov 2011, at 04:33, Michael
Truog wrote:</div>
<br>
<blockquote type="cite">
<div>I was looking at Erlang priority
queue implementations and the
Riak/RabbitMQ one seemed a bit slow.
I have a different implementation
with the same API here: <a
moz-do-not-send="true"
href="https://github.com/okeuday/pqueue/blob/master/src/pqueue.erl">https://github.com/okeuday/pqueue/blob/master/src/pqueue.erl</a><br>
<br>
The results from my test are here: <a
moz-do-not-send="true"
href="http://okeuday.livejournal.com/19187.html">http://okeuday.livejournal.com/19187.html</a><br>
<br>
The implementation has "in"
operations that are roughly 3 times
faster (300%), however, the "out"
operation became roughly 30% slower.
So, as long as the priority queue
is storing a decent amount of items,
this data structure should provide
better speed. The implementation is
limited to a specific priority
range: -20 (high) to 20 (low).<br>
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</blockquote>
</div>
<br>
<div>
<div>Ulf Wiger, CTO, Erlang Solutions,
Ltd.</div>
<div><a moz-do-not-send="true"
href="http://erlang-solutions.com/">http://erlang-solutions.com</a></div>
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</div>
<br>
</div>
</div>
</blockquote>
</div>
<br>
<div> <span>
<div>Ulf Wiger, CTO, Erlang Solutions, Ltd.</div>
<div><a moz-do-not-send="true"
href="http://erlang-solutions.com/">http://erlang-solutions.com</a></div>
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</blockquote>
<br>
</div>
</blockquote>
</div>
<br>
<div>
<span>
<div>Ulf Wiger, CTO, Erlang Solutions, Ltd.</div>
<div><a moz-do-not-send="true"
href="http://erlang-solutions.com">http://erlang-solutions.com</a></div>
<div><br>
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