Re: GEQO: ERX

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From: Tobias Zahn <tobias-zahn(at)arcor(dot)de>
To: pgsql-hackers(at)postgresql(dot)org
Subject: GEQO: ERX
Date: 2009-04-20 19:59:25
Message-ID: 49ECD41D.3000009@arcor.de
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Hello,
I was digging through the optimizer code and have a question regarding
the edge recombination crossover (ERX) of the GEQO. It might be
completely stupid and therefore I apologize for this in advance.

As far as I understand it, the idea of the ERX is the minimization of
edge failures. When reading in geqo_main.c and geqo_erx.c, it seams that
every iterative round (generation) it is checked by gimme_tour() if
there where any edge failures. When I understand the algorithm right,
there should be no edge failures.
Therefore I think about NOT checking for edge failures anymore, to save
some time. (If it just to make sure, it could be done only once in the
end.) Might that work or do I have some errors in my thoughts?

Thanks in advance,
Tobias


From: Tom Lane <tgl(at)sss(dot)pgh(dot)pa(dot)us>
To: Tobias Zahn <tobias-zahn(at)arcor(dot)de>
Cc: pgsql-hackers(at)postgresql(dot)org
Subject: Re: GEQO: ERX
Date: 2009-05-02 15:37:16
Message-ID: 15658.1241278636@sss.pgh.pa.us
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Tobias Zahn <tobias-zahn(at)arcor(dot)de> writes:
> I didn't not get any response to my initial message below. Now I am
> wondering if nobody is into the optimizer or if my question was just too
> stupid. Could you please give me some clues? Your help would really be
> appreciated.

Well, nobody's into GEQO very much. I took a quick look and didn't
think that deleting the ERX support would save anything noticeable,
but you're welcome to try it if you think different.

The real problem with working on GEQO, in my humble opinion, is that
it's throwing good effort after bad. That module doesn't need marginal
fixing, it needs throwing away and rewriting from scratch. Bad enough
that it's convoluted and full of dead (experimental?) code; but I don't
even believe that it's based on a good analogy. The planning problem
is not all that much like traveling salesman problems, so heuristics
designed for TSP are of pretty questionable usefulness to start with.
That complaint could have been refuted if the module performed well,
but in fact if you check the archives you'll find many many complaints
about it --- its ability to find good plans seems to be mostly dependent
on luck.

My knowledge of AI search algorithms is about 20 years obsolete, but
last I heard simulated annealing had overtaken genetic algorithms for
many purposes. It might be interesting to try a rewrite based on SA;
or maybe there's something better out there now.

regards, tom lane


From: Tobias Zahn <tobias-zahn(at)arcor(dot)de>
To: pgsql-hackers(at)postgresql(dot)org
Subject: Re: GEQO: ERX
Date: 2009-05-02 15:45:22
Message-ID: 49FC6A92.7000302@arcor.de
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Hello again,
I didn't not get any response to my initial message below. Now I am
wondering if nobody is into the optimizer or if my question was just too
stupid. Could you please give me some clues? Your help would really be
appreciated.

Regards,
Tobias

> Hello,
> I was digging through the optimizer code and have a question regarding
> the edge recombination crossover (ERX) of the GEQO. It might be
> completely stupid and therefore I apologize for this in advance.
>
> As far as I understand it, the idea of the ERX is the minimization of
> edge failures. When reading in geqo_main.c and geqo_erx.c, it seams that
> every iterative round (generation) it is checked by gimme_tour() if
> there where any edge failures. When I understand the algorithm right,
> there should be no edge failures.
> Therefore I think about NOT checking for edge failures anymore, to save
> some time. (If it just to make sure, it could be done only once in the
> end.) Might that work or do I have some errors in my thoughts?
>
> Thanks in advance,
> Tobias
>


From: Dimitri Fontaine <dfontaine(at)hi-media(dot)com>
To: Tom Lane <tgl(at)sss(dot)pgh(dot)pa(dot)us>
Cc: Tobias Zahn <tobias-zahn(at)arcor(dot)de>, pgsql-hackers(at)postgresql(dot)org
Subject: Re: GEQO: ERX
Date: 2009-05-02 18:50:53
Message-ID: 4CC854A3-58FE-4987-B5FC-0B193CC4382A@hi-media.com
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Hi,

Le 2 mai 09 à 17:37, Tom Lane a écrit :
> My knowledge of AI search algorithms is about 20 years obsolete, but
> last I heard simulated annealing had overtaken genetic algorithms for
> many purposes. It might be interesting to try a rewrite based on SA;
> or maybe there's something better out there now.

I've done very very few courses in the domain, and was tough SA too
(about 10 years ago). But what I gathered more recently was that it's
already being obsoleted by fuzzy logic ideas, which implementations
are more and more reliable.

The idea would be to offer typical queries and possible plans, and to
tell apart the very good ones from the good and pretty bad ones. This
would serve as a model for the fuzzy logic engine to take decisions
and be able to give back best possible plan (as showed) for a given
input set (the query).

I'm very unclear how to better specify learning methods or models,
etc, and probably I should have left this part away. But it well seems
it's the "better out there now" trend.
Recreating the same end-product from a given recipe and new constraint
(raw milk enabled industrial products is forbidden in this country) is
an example of application.

Regards,
--
dim


From: Robert Haas <robertmhaas(at)gmail(dot)com>
To: Tom Lane <tgl(at)sss(dot)pgh(dot)pa(dot)us>
Cc: Tobias Zahn <tobias-zahn(at)arcor(dot)de>, pgsql-hackers(at)postgresql(dot)org
Subject: Re: GEQO: ERX
Date: 2009-05-03 20:03:07
Message-ID: 603c8f070905031303t770724d6h674e4ba049acc65c@mail.gmail.com
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On Sat, May 2, 2009 at 11:37 AM, Tom Lane <tgl(at)sss(dot)pgh(dot)pa(dot)us> wrote:
> Tobias Zahn <tobias-zahn(at)arcor(dot)de> writes:
>> I didn't not get any response to my initial message below. Now I am
>> wondering if nobody is into the optimizer or if my question was just too
>> stupid. Could you please give me some clues? Your help would really be
>> appreciated.
>
> Well, nobody's into GEQO very much.  I took a quick look and didn't
> think that deleting the ERX support would save anything noticeable,
> but you're welcome to try it if you think different.
>
> The real problem with working on GEQO, in my humble opinion, is that
> it's throwing good effort after bad.  That module doesn't need marginal
> fixing, it needs throwing away and rewriting from scratch.  Bad enough
> that it's convoluted and full of dead (experimental?) code; but I don't
> even believe that it's based on a good analogy.   The planning problem
> is not all that much like traveling salesman problems, so heuristics
> designed for TSP are of pretty questionable usefulness to start with.
> That complaint could have been refuted if the module performed well,
> but in fact if you check the archives you'll find many many complaints
> about it --- its ability to find good plans seems to be mostly dependent
> on luck.
>
> My knowledge of AI search algorithms is about 20 years obsolete, but
> last I heard simulated annealing had overtaken genetic algorithms for
> many purposes.  It might be interesting to try a rewrite based on SA;
> or maybe there's something better out there now.

There's a 1997 article on this topic that's pretty interesting.

Heuristic and randomized optimization for the join ordering problem
http://reference.kfupm.edu.sa/content/h/e/heuristic_and_randomized_optimization_fo_87585.pdf

Here's the basic conclusion:

"If good solutions are of highest importance, Two-Phase Optimization,
the algorithm that performed best in our experiments, is a very good
choice; other Simulated Annealing variants, for instance Toured
Simulated Annealing (TSA, LVZ93]), that we did not implement, are
likely to achieve quite similar results. The 'pure' Simulated
Annealing algorithm has a much higher running time without yielding
significantly better solutions. If short running time is more
important, Iterative Improvement (IIIO), the genetic algo- rithm
(BushyGenetic), and, to a lesser extent, Two-Phase Optimization (2PO)
are feasible alternatives."

I'm not sure if there's anything more recent out there.

...Robert


From: Tobias Zahn <tobias-zahn(at)arcor(dot)de>
To: Robert Haas <robertmhaas(at)gmail(dot)com>
Cc: Tom Lane <tgl(at)sss(dot)pgh(dot)pa(dot)us>, pgsql-hackers(at)postgresql(dot)org
Subject: Re: GEQO: ERX
Date: 2009-05-13 20:14:25
Message-ID: 4A0B2A21.1000908@arcor.de
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Hello,
thank you for posting the paper, it was quite interesting to read. I
think it would be a good idea to give the two-phase optimization a try.
As far as I know and understand the current (geqo) optimizer source,
many important parts are already there. For example, we can calculate
the costs of a given join order. Therefore, it would only be necessary
to write an algorithm witch chooses the right input for the cost function.
I would be interested in your opinion.

Regards,
Tobias

Robert Haas schrieb:
> On Sat, May 2, 2009 at 11:37 AM, Tom Lane <tgl(at)sss(dot)pgh(dot)pa(dot)us> wrote:
>> Tobias Zahn <tobias-zahn(at)arcor(dot)de> writes:
>>> I didn't not get any response to my initial message below. Now I am
>>> wondering if nobody is into the optimizer or if my question was just too
>>> stupid. Could you please give me some clues? Your help would really be
>>> appreciated.
>> Well, nobody's into GEQO very much. I took a quick look and didn't
>> think that deleting the ERX support would save anything noticeable,
>> but you're welcome to try it if you think different.
>>
>> The real problem with working on GEQO, in my humble opinion, is that
>> it's throwing good effort after bad. That module doesn't need marginal
>> fixing, it needs throwing away and rewriting from scratch. Bad enough
>> that it's convoluted and full of dead (experimental?) code; but I don't
>> even believe that it's based on a good analogy. The planning problem
>> is not all that much like traveling salesman problems, so heuristics
>> designed for TSP are of pretty questionable usefulness to start with.
>> That complaint could have been refuted if the module performed well,
>> but in fact if you check the archives you'll find many many complaints
>> about it --- its ability to find good plans seems to be mostly dependent
>> on luck.
>>
>> My knowledge of AI search algorithms is about 20 years obsolete, but
>> last I heard simulated annealing had overtaken genetic algorithms for
>> many purposes. It might be interesting to try a rewrite based on SA;
>> or maybe there's something better out there now.
>
> There's a 1997 article on this topic that's pretty interesting.
>
> Heuristic and randomized optimization for the join ordering problem
> http://reference.kfupm.edu.sa/content/h/e/heuristic_and_randomized_optimization_fo_87585.pdf
>
> Here's the basic conclusion:
>
> "If good solutions are of highest importance, Two-Phase Optimization,
> the algorithm that performed best in our experiments, is a very good
> choice; other Simulated Annealing variants, for instance Toured
> Simulated Annealing (TSA, LVZ93]), that we did not implement, are
> likely to achieve quite similar results. The 'pure' Simulated
> Annealing algorithm has a much higher running time without yielding
> significantly better solutions. If short running time is more
> important, Iterative Improvement (IIIO), the genetic algo- rithm
> (BushyGenetic), and, to a lesser extent, Two-Phase Optimization (2PO)
> are feasible alternatives."
>
> I'm not sure if there's anything more recent out there.
>
> ...Robert
>


From: Robert Haas <robertmhaas(at)gmail(dot)com>
To: Tobias Zahn <tobias-zahn(at)arcor(dot)de>
Cc: Tom Lane <tgl(at)sss(dot)pgh(dot)pa(dot)us>, pgsql-hackers(at)postgresql(dot)org
Subject: Re: GEQO: ERX
Date: 2009-05-13 20:37:17
Message-ID: 603c8f070905131337n355d36e9qbfba973439a1062a@mail.gmail.com
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On Wed, May 13, 2009 at 4:14 PM, Tobias Zahn <tobias-zahn(at)arcor(dot)de> wrote:
> Hello,
> thank you for posting the paper, it was quite interesting to read. I
> think it would be a good idea to give the two-phase optimization a try.
> As far as I know and understand the current (geqo) optimizer source,
> many important parts are already there. For example, we can calculate
> the costs of a given join order. Therefore, it would only be necessary
> to write an algorithm witch chooses the right input for the cost function.
> I would be interested in your opinion.

I'm very interested in any improvements we can make to planning large
join nests. Unfortunately the paper seems to conclude that it's not
really feasible to use heuristics, as had been my hope, but I'd be
very interested in any other approaches we can come up with. I
probably do not have time to implement anything myself, but I'm happy
to help with ideas and code review.

...Robert


From: Adriano Lange <alange0001(at)gmail(dot)com>
To: Robert Haas <robertmhaas(at)gmail(dot)com>
Cc: Tobias Zahn <tobias-zahn(at)arcor(dot)de>, Tom Lane <tgl(at)sss(dot)pgh(dot)pa(dot)us>, pgsql-hackers(at)postgresql(dot)org
Subject: Re: GEQO: ERX
Date: 2009-05-19 21:38:04
Message-ID: 4A1326BC.1030609@gmail.com
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Robert Haas escreveu:
> On Wed, May 13, 2009 at 4:14 PM, Tobias Zahn <tobias-zahn(at)arcor(dot)de> wrote:
>> Hello,
>> thank you for posting the paper, it was quite interesting to read. I
>> think it would be a good idea to give the two-phase optimization a try.
>> As far as I know and understand the current (geqo) optimizer source,
>> many important parts are already there. For example, we can calculate
>> the costs of a given join order. Therefore, it would only be necessary
>> to write an algorithm witch chooses the right input for the cost function.
>> I would be interested in your opinion.
>
> I'm very interested in any improvements we can make to planning large
> join nests. Unfortunately the paper seems to conclude that it's not
> really feasible to use heuristics, as had been my hope, but I'd be
> very interested in any other approaches we can come up with. I
> probably do not have time to implement anything myself, but I'm happy
> to help with ideas and code review.
>

I implemented the 2PO algorithm last month but I didn't have much time
to do an extensive test and to comment all code. The code was posted in
this list in a previous thread. In that occasion, I was interested in a
kind of cache structure to avoid the constructing a complete RelOptInfo
from scratch every time when the cheapest total_cost must be calculated
(this occur in GEQO).

I’m sending a patch for the 8.3 release.

I also changed some GUC variables to facilitate some tests:
(remove) geqo
(remove) geqo_threshold
(add) ljqo_enable (bool) – activate Large Join Query Optimizer
(add) ljqo_algorithm {geqo|twopo}
(add) ljqo_threshold (int) – like geqo_threshold
(add) twopo_heuristic_states (bool) – initial heuristic states
(add) twopo_ii_stop (int) – II phase loop
(add) twopo_sa_phase (bool) – enable SA phase
(add) twopo_sa_initial_temperature (float)
(add) twopo_sa_temperature_reduction (float)
(add) twopo_sa_equilibrium (int)

In my little tests, this algorithm seems equal or worse than geqo,
except when using heuristic in order to bias the initial state. Maybe
some tunings are needed but I prefer spend yet some time reading more
about the compressed annealing, cited in TODO list. Anyway, I think that
to build another annealing-like algorithm might be easier if some
structures and functions in 2PO source code are correct.

Sincerely,

Adriano Lange


From: Adriano Lange <alange0001(at)gmail(dot)com>
To: Robert Haas <robertmhaas(at)gmail(dot)com>
Cc: Tobias Zahn <tobias-zahn(at)arcor(dot)de>, Tom Lane <tgl(at)sss(dot)pgh(dot)pa(dot)us>, pgsql-hackers(at)postgresql(dot)org
Subject: Re: GEQO: ERX
Date: 2009-05-19 21:48:09
Message-ID: 4A132919.3040708@gmail.com
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Adriano Lange escreveu:
> I implemented the 2PO algorithm last month but I didn't have much time
> to do an extensive test and to comment all code. The code was posted in
> this list in a previous thread. In that occasion, I was interested in a
> kind of cache structure to avoid the constructing a complete RelOptInfo
> from scratch every time when the cheapest total_cost must be calculated
> (this occur in GEQO).
>
> I’m sending a patch for the 8.3 release.

I forgot it.

>
> I also changed some GUC variables to facilitate some tests:
> (remove) geqo
> (remove) geqo_threshold
> (add) ljqo_enable (bool) – activate Large Join Query Optimizer
> (add) ljqo_algorithm {geqo|twopo}
> (add) ljqo_threshold (int) – like geqo_threshold
> (add) twopo_heuristic_states (bool) – initial heuristic states
> (add) twopo_ii_stop (int) – II phase loop
> (add) twopo_sa_phase (bool) – enable SA phase
> (add) twopo_sa_initial_temperature (float)
> (add) twopo_sa_temperature_reduction (float)
> (add) twopo_sa_equilibrium (int)
>
> In my little tests, this algorithm seems equal or worse than geqo,
> except when using heuristic in order to bias the initial state. Maybe
> some tunings are needed but I prefer spend yet some time reading more
> about the compressed annealing, cited in TODO list. Anyway, I think that
> to build another annealing-like algorithm might be easier if some
> structures and functions in 2PO source code are correct.
>
> Sincerely,
>
> Adriano Lange
>

Attachment Content-Type Size
postgresql-8.3.1-twopo-20090421.patch text/x-patch 37.7 KB

From: Tobias Zahn <tobias-zahn(at)arcor(dot)de>
To: Adriano Lange <alange0001(at)gmail(dot)com>
Cc: Robert Haas <robertmhaas(at)gmail(dot)com>, Tom Lane <tgl(at)sss(dot)pgh(dot)pa(dot)us>, pgsql-hackers(at)postgresql(dot)org
Subject: Re: GEQO: ERX
Date: 2009-05-20 15:52:27
Message-ID: 4A14273B.3050206@arcor.de
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Hello Adriano,
thank you very much for posting your patch. I think it will help to make
further work easier, too. I hope you don't mind when I ask you some
questions.

When you said that this new approach is worse or equal than GEQO, did
you refer to performance or to the quality of results?
Why do you think that compressed annealing might be the better approach?

TIA and best regards,
Tobias Zahn

Adriano Lange schrieb:
> Robert Haas escreveu:
>> On Wed, May 13, 2009 at 4:14 PM, Tobias Zahn <tobias-zahn(at)arcor(dot)de>
>> wrote:
>>> Hello,
>>> thank you for posting the paper, it was quite interesting to read. I
>>> think it would be a good idea to give the two-phase optimization a try.
>>> As far as I know and understand the current (geqo) optimizer source,
>>> many important parts are already there. For example, we can calculate
>>> the costs of a given join order. Therefore, it would only be necessary
>>> to write an algorithm witch chooses the right input for the cost
>>> function.
>>> I would be interested in your opinion.
>>
>> I'm very interested in any improvements we can make to planning large
>> join nests. Unfortunately the paper seems to conclude that it's not
>> really feasible to use heuristics, as had been my hope, but I'd be
>> very interested in any other approaches we can come up with. I
>> probably do not have time to implement anything myself, but I'm happy
>> to help with ideas and code review.
>>
>
> I implemented the 2PO algorithm last month but I didn't have much time
> to do an extensive test and to comment all code. The code was posted in
> this list in a previous thread. In that occasion, I was interested in a
> kind of cache structure to avoid the constructing a complete RelOptInfo
> from scratch every time when the cheapest total_cost must be calculated
> (this occur in GEQO).
>
> I’m sending a patch for the 8.3 release.
>
> I also changed some GUC variables to facilitate some tests:
> (remove) geqo
> (remove) geqo_threshold
> (add) ljqo_enable (bool) – activate Large Join Query Optimizer
> (add) ljqo_algorithm {geqo|twopo}
> (add) ljqo_threshold (int) – like geqo_threshold
> (add) twopo_heuristic_states (bool) – initial heuristic states
> (add) twopo_ii_stop (int) – II phase loop
> (add) twopo_sa_phase (bool) – enable SA phase
> (add) twopo_sa_initial_temperature (float)
> (add) twopo_sa_temperature_reduction (float)
> (add) twopo_sa_equilibrium (int)
>
> In my little tests, this algorithm seems equal or worse than geqo,
> except when using heuristic in order to bias the initial state. Maybe
> some tunings are needed but I prefer spend yet some time reading more
> about the compressed annealing, cited in TODO list. Anyway, I think that
> to build another annealing-like algorithm might be easier if some
> structures and functions in 2PO source code are correct.
>
> Sincerely,
>
> Adriano Lange
>
>


From: Adriano Lange <alange0001(at)gmail(dot)com>
To: Tobias Zahn <tobias-zahn(at)arcor(dot)de>
Cc: Robert Haas <robertmhaas(at)gmail(dot)com>, Tom Lane <tgl(at)sss(dot)pgh(dot)pa(dot)us>, pgsql-hackers(at)postgresql(dot)org
Subject: Re: GEQO: ERX
Date: 2009-05-21 03:06:15
Message-ID: 4A14C527.7000904@gmail.com
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Hi

Tobias Zahn escreveu:
> Hello Adriano,
> thank you very much for posting your patch. I think it will help to make
> further work easier, too. I hope you don't mind when I ask you some
> questions.
>
> When you said that this new approach is worse or equal than GEQO, did
> you refer to performance or to the quality of results?

Not exactly this approach, but the implemented (and not configured)
algorithm was worse than GEQO in a little test made. I just used a
sequence of 8 executions of a query with 18 relations for each
algorithm. The costs generated by GEQO was little better than 2PO, in
average and standard deviation. But 8 executions and 1 query don't prove
anything. I want to make some further tests, but this little difference
seems good for me.

> Why do you think that compressed annealing might be the better approach?

I don't think if compressed annealing is better or not. I don't read
about it yet.

However, an optimizer can be better in a context but worse in another.

Regards,
Adriano


From: Bruce Momjian <bruce(at)momjian(dot)us>
To: Adriano Lange <alange0001(at)gmail(dot)com>
Cc: Tobias Zahn <tobias-zahn(at)arcor(dot)de>, Robert Haas <robertmhaas(at)gmail(dot)com>, Tom Lane <tgl(at)sss(dot)pgh(dot)pa(dot)us>, pgsql-hackers(at)postgresql(dot)org
Subject: Re: GEQO: ERX
Date: 2009-05-28 02:04:25
Message-ID: 200905280204.n4S24PJ19673@momjian.us
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Is this a TODO item?

---------------------------------------------------------------------------

Adriano Lange wrote:
> Hi
>
> Tobias Zahn escreveu:
> > Hello Adriano,
> > thank you very much for posting your patch. I think it will help to make
> > further work easier, too. I hope you don't mind when I ask you some
> > questions.
> >
> > When you said that this new approach is worse or equal than GEQO, did
> > you refer to performance or to the quality of results?
>
> Not exactly this approach, but the implemented (and not configured)
> algorithm was worse than GEQO in a little test made. I just used a
> sequence of 8 executions of a query with 18 relations for each
> algorithm. The costs generated by GEQO was little better than 2PO, in
> average and standard deviation. But 8 executions and 1 query don't prove
> anything. I want to make some further tests, but this little difference
> seems good for me.
>
> > Why do you think that compressed annealing might be the better approach?
>
> I don't think if compressed annealing is better or not. I don't read
> about it yet.
>
> However, an optimizer can be better in a context but worse in another.
>
> Regards,
> Adriano
>
> --
> Sent via pgsql-hackers mailing list (pgsql-hackers(at)postgresql(dot)org)
> To make changes to your subscription:
> http://www.postgresql.org/mailpref/pgsql-hackers

--
Bruce Momjian <bruce(at)momjian(dot)us> http://momjian.us
EnterpriseDB http://enterprisedb.com

+ If your life is a hard drive, Christ can be your backup. +


From: Tom Lane <tgl(at)sss(dot)pgh(dot)pa(dot)us>
To: Bruce Momjian <bruce(at)momjian(dot)us>
Cc: Adriano Lange <alange0001(at)gmail(dot)com>, Tobias Zahn <tobias-zahn(at)arcor(dot)de>, Robert Haas <robertmhaas(at)gmail(dot)com>, pgsql-hackers(at)postgresql(dot)org
Subject: Re: GEQO: ERX
Date: 2009-05-28 02:11:03
Message-ID: 23825.1243476663@sss.pgh.pa.us
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Bruce Momjian <bruce(at)momjian(dot)us> writes:
> Is this a TODO item?

We already have a TODO item about replacing GEQO.

However, linking to this thread might be more useful than the 404 that's
there now...

regards, tom lane


From: Bruce Momjian <bruce(at)momjian(dot)us>
To: Tom Lane <tgl(at)sss(dot)pgh(dot)pa(dot)us>
Cc: Adriano Lange <alange0001(at)gmail(dot)com>, Tobias Zahn <tobias-zahn(at)arcor(dot)de>, Robert Haas <robertmhaas(at)gmail(dot)com>, pgsql-hackers(at)postgresql(dot)org
Subject: Re: GEQO: ERX
Date: 2009-05-28 02:15:43
Message-ID: 200905280215.n4S2FhE05428@momjian.us
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Tom Lane wrote:
> Bruce Momjian <bruce(at)momjian(dot)us> writes:
> > Is this a TODO item?
>
> We already have a TODO item about replacing GEQO.
>
> However, linking to this thread might be more useful than the 404 that's
> there now...

Removed and added.

--
Bruce Momjian <bruce(at)momjian(dot)us> http://momjian.us
EnterpriseDB http://enterprisedb.com

+ If your life is a hard drive, Christ can be your backup. +