- From: jorge perez <jorge.perez.rojas@gmail.com>
- Date: Fri, 27 Jan 2012 11:51:45 -0300
- 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 Friday, 27 January 2012 14:52:22 UTC