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Re: Fwd: Comments about the semantics of property paths

From: Lee Feigenbaum <lee@thefigtrees.net>
Date: Sun, 29 Jan 2012 14:03:40 -0500
Message-ID: <4F25980C.4030407@thefigtrees.net>
To: Andy Seaborne <andy.seaborne@epimorphics.com>
CC: SPARQL Working Group <public-rdf-dawg@w3.org>
I'd suggest we discuss on our call this week.


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
> 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 19:04:11 UTC

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