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Re: Fwd: Comments about the semantics of property paths

From: Andy Seaborne <andy.seaborne@epimorphics.com>
Date: Sun, 29 Jan 2012 19:28:10 +0000
Message-ID: <4F259DCA.60007@epimorphics.com>
To: Lee Feigenbaum <lee@thefigtrees.net>
CC: SPARQL Working Group <public-rdf-dawg@w3.org>
It would be useful but I wasn't expecting a change to the plan of 
approving tests and progressing the graph store protocol discussions.

End of last call for query is Feb 6th - I don't expect we will be 
replying until after that point anyway, but, if there's time, we can 
make a start discussing it.

	Andy

On 29/01/12 19:03, Lee Feigenbaum wrote:
> I'd suggest we discuss on our call this week.
>
> Lee
>
> On 1/28/2012 12:38 PM, Andy Seaborne wrote:
>> A previous conversation of these issues includes:
>>
>> http://lists.w3.org/Archives/Public/public-rdf-dawg-comments/2011Feb/0005.html
>>
>>
>>
>> where the WG points out:
>> 1/ That aggregation may yield confusing results to a natural query
>> 2/ That an optimizer may be given further information via a sub-query
>> and DISTINCT.
>>
>> The purchase order example seems to me to be a reasonable expectation of
>> any spreadsheet user. The same price is arrived at several times (two
>> ways: via two :item1's and two uses of the same literal 2).
>>
>> There are two sets of use cases: one set where duplicates are essential,
>> and one set where they are redundant.
>>
>> Jorge's reply then:
>>
>> http://lists.w3.org/Archives/Public/public-rdf-dawg-comments/2011Feb/0012.html
>>
>>
>>
>> acknowledged the points in the response.
>>
>> Andy
>>
>> -------- Original Message --------
>> Subject: Comments about the semantics of property paths
>> Resent-Date: Fri, 27 Jan 2012 14:52:22 +0000
>> Resent-From: public-rdf-dawg-comments@w3.org
>> Date: Fri, 27 Jan 2012 11:51:45 -0300
>> From: jorge perez <jorge.perez.rojas@gmail.com>
>> To: public-rdf-dawg-comments@w3.org
>> CC: Marcelo Arenas <marcelo.arenas1@gmail.com>, Sebastián Conca
>> <sconca87@gmail.com>, jorge perez <jorge.perez.rojas@gmail.com>
>>
>> Dear DAWG members,
>>
>> We have some comments regarding the semantics of property paths. We
>> know that this issue has been raised before, but we think that we can
>> provide substantial new information to reconsider it.
>>
>> We have conducted a thorough study of the current semantics of
>> property paths including an empirical analysis. All our results are in
>> a paper that has been accepted in WWW 2012. You can find a
>> copy of the extended version of this paper at
>> http://www.dcc.uchile.cl/~jperez/sub-www-ext.pdf. Given the tight
>> schedule of the group, we think that it might be useful to make these
>> results public for the group before we have a final published version.
>>
>> As a summary we can provide two main comments, one from a practical
>> perspective and another from a theoretical perspective.
>>
>> -----------
>>
>> - Comment 1: Poor performance of current engines.
>> =================================================
>> We tested 4 implementations of property paths: Jena, RDF::Query,
>> Sesame, and KGram-Corese (details on the experimental setting can be
>> found at http://www.dcc.uchile.cl/~jperez/www_repeatability/). A first
>> set of experiments was with synthetic data and other with real data.
>>
>> In both cases the implementations were not capable to handle even
>> small data for the most simple property path queries.
>>
>> Case A)
>> We tested RDF data representing complete graphs. No implementation was
>> able to handle a graph with 13 nodes for a query with a single
>> property path of the form (:P)*
>>
>> data1: http://www.dcc.uchile.cl/~jperez/www_repeatability/clique13.n3
>> query1: http://www.dcc.uchile.cl/~jperez/www_repeatability/Cliq-1.rq
>>
>> See Figure 1 in the paper for the performance of all implementations
>> below 13 nodes. The figure suggests that the evaluation time for these
>> implementations growths doubly-exponentially w.r.t. the size of the
>> input.
>>
>> Case B)
>> We tested real RDF data crawled from a small set of foaf documents. We
>> started from Axel's foaf document and retrieve friends, friends of
>> friends, etc. following foaf:knows links, and constructed several test
>> cases. In this case, no implementation was able to handle an RDF graph
>> of 14KB for a query with a single property path (foaf:knows)*
>>
>> data2: http://www.dcc.uchile.cl/~jperez/www_repeatability/E.n3
>> query2: http://www.dcc.uchile.cl/~jperez/www_repeatability/Foaf-1.rq
>>
>> See Table 1 in the paper for the performance of all implementations.
>>
>> - Comment 2: High Computational Complexity.
>> ===========================================
>> We prove in the paper that for the current semantics of property paths
>> in SPARQL the complexity of evaluation is double-exponential (Lemma
>> 5.4 and Theorem 5.5). Given that property paths require counting
>> paths, we measure the complexity by making use of counting complexity
>> classes. The technical result is that SPARQL 1.1 evaluation is not
>> even inside #P (Theorem 5.5), where #P is the counting complexity
>> class associated to NP (a prototypical #P-complete problem is the problem
>> of computing the number of truth assignments that satisfies a
>> propositional
>> formula, which is more complicated than the prototypical NP-complete
>> problem
>> which is to verify whether there exists at least one truth assignment
>> that
>> satisfies a propositional formula). Thus, in informal terms, we prove
>> that
>> SPARQL 1.1 evaluation considering counting is even more complex than
>> solving an NP-complete problem.
>>
>> We also prove that if only the input data is considered to measure the
>> complexity of the problem, then the evaluation problem is #P-hard.
>> Notice that without property paths, the evaluation problem for SPARQL
>> can be solved in polynomial time (if the complexity is measured only in
>> terms of the size of the data).
>>
>> ------------
>>
>> Discussion
>> ==========
>>
>> One of the main conclusions that one can draw from our results is that
>> the poor performance exhibited in Cases A) and B) above is not a
>> problem of the particular implementations but a problem of the
>> specification itself, as our theoretical results imply that every
>> implementation that follows the current specification of SPARQL 1.1
>> would have the same poor behavior.
>>
>> Our results also show that the main source of complexity is the
>> requirement of counting paths, and in particular the procedure ALP
>> which is the one that gives the semantics for counting. Essentially,
>> the counting mechanism produces a number of duplicates that in some
>> cases are beyond any naturally feasible number. Table 7 in the paper
>> shows a worst case analysis. For instance, for the case
>>
>> data3: http://www.dcc.uchile.cl/~jperez/www_repeatability/clique7.n3
>> query3: http://www.dcc.uchile.cl/~jperez/www_repeatability/Cliq-2.rq
>>
>> we formally prove that any implementation that follows the current
>> specification should produce an output of 79 Yottabytes (79 trillion
>> Terabytes), and thus would not fit in any reasonable storage device.
>> Please notice that unfeasible counting can also be obtained with real
>> data. For example, for the case
>>
>> data4: http://www.dcc.uchile.cl/~jperez/www_repeatability/D.n3
>> query2: http://www.dcc.uchile.cl/~jperez/www_repeatability/Foaf-1.rq
>>
>> ARQ (which was the only implementation that was able to handle this
>> case in less than one hour) produced an output of 587MB. Notice that
>> data3 is of only 13.2KB. Table 6 in the paper shows the running time
>> and the output size. Please notice that this experiment is with real
>> data and it is highly probable that property paths will be used in
>> practice with this type of queries.
>>
>> It is worth mentioning that our group is not the only one that have
>> formally studied property-path semantics according to the current
>> specification, and that have shown negative results about the complexity
>> of evaluating it. We are aware that Katja Losemann and Wim Martens
>> obtained similar results independently from us. Wim Martens gave a
>> talk about this called "The complexity of evaluating path expressions
>> in SPARQL" in a Dagstuhl seminar. In that work, the authors also
>> studied property-path expressions of the form :P{m,n}, and show that
>> the complexity of evaluating them is very high.
>>
>> We think that we have provided substantial new information to
>> reconsider the issue of property path semantics. We have several other
>> comments, but we think that the two comments above are the most
>> important to consider, and we are open to continue the discussion with
>> the group and, if necessary, cooperate with the group to make a proposal
>> for property path evaluation that can have an efficient evaluation
>> method.
>>
>> Best regards,
>>
>> Marcelo Arenas
>> Sebastián Conca
>> Jorge Pérez
>>
>>
>>
Received on Sunday, 29 January 2012 19:28:39 GMT

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