On The Marriage of SPARQL and Keywords
Peng Peng, Lei Zou, Dongyan Zhao Peking University, China; { pku09pp,zoulei,zhaodongyan}@pku.edu.cn
ABSTRACT whole schema; thus, it may not be possible to specify exact query Although SPARQL has been the predominant query language over criteria. The following example illustrates the challenges. RDF graphs, some query intentions cannot be well captured by only Philadelphia(film) Actor EXAMPLE 1. Find all actors starringPhiladelphia(film in film Philadelphia) Actor, who using SPARQL syntax. On the other hand, the keyword search en- are related to “Academy Award” and “Goldentype Globe Award”. As- type actedIn joys widespread usage because of its intuitive way of specifying in- actedIn type type sume that we do not know the exact URIs corresponding to “Academy formation needs but suffers from the problem of low precision. To Film ?x Film ?x Award” and “Golden Globe Award”. Furthermore, there is no pre- maximize the advantages of both SPARQL and keyword search, we cise predicate corresponding to “related to”. introduce a novel paradigm that combines both of them and propose a hybrid query (called an SK query) that integrates SPARQL and Select ?a where{ ?a ?p ?str. keyword search. In order to answer SK queries efficiently, a struc- SPARQL: ?a type Actor. tural index is devised, based on a novel integrated query algorithm Select ?a where{ ?a actedIn Philadelphia(film). is proposed. We evaluate our method in large real RDF graphs and ?a type Actor. Philadelphia(film) type Film. experiments demonstrate both effectiveness and efficiency of our ?a actedIn Philadelphia(film). FILTER regex(?str, "(Academy Award)| Philadelphia(film) type Film} method. (Golden Globe Award)")} (a) Q1 (b) Q2 1. INTRODUCTION Figure 2: Example SPARQL Queries As more and more knowledge bases become available, the ques- There are two issues in this example. First, since we do not know tion of how end users can access this body of knowledge becomes the URIs of “Academy Award” and “Golden Globe Award”, we of crucial importance. As the de facto standard of a knowledge should provide a keyword search paradigm that maps the keywords base, RDF (Resource Description Framework) repository is a col- to the corresponding entities or classes in RDF graphs. Existing lection of triples, denoted as h subject, predicate, object i. An RDF SPARQL syntax only supports the regular expression, as shown in repository can be represented as a graph, where subjects and ob- Figure 2. More typographic or linguistic distances, such as string jects are vertices connected by labeled edges (i.e., predicates). Fig- edit distance [9] and google similarity distance [6], are desirable. ure 1 shows an example RDF dataset and the corresponding RDF The second issue is that there is no precise predicate correspond- graph, which is a part of a well-known knowledge base Yago [27]. ing to “related to”. A possible solution is to use “unknown” pred- All subjects and objects correspond to vertices and predicates cor- icate (i.e., a variable at the predicate position), but, it only finds respond to edge labels. The numbers besides the vertices are IDs, one-hop relations. Figure 2(b) shows a SPARQL query with un- and they are introduced for the easy presentation. known predicate and the regular expression FILTER. However, it As we know, SPARQL query language is a standard way to ac- fails to finding the multiple-hop relations, which may also be infor- cess RDF data and is based on the subgraph (homomorphism) match mative to users. For example, Antonio Banderas, an actor starring semantic [25]. Figure 2(a) shows an example of SPARQL query in Philadelphia film, whose wife won “Golden Globe Award”. This and its corresponding query graph graph is shown in Figure 1(c). is also a possible interesting result to users, but, this is a two-hop arXiv:1411.6335v3 [cs.DB] 30 Nov 2014 The query semantics of the example SPARQL is “finding all actors relation between Antonio Banderas and “Golden Globe Award”. starring in film Philadelphia”, To enable to use SPARQL, users In contrast, keyword search [2, 17, 15, 10, 19, 18] on graphs should have full knowledge of the whole RDF schema. For exam- provides an intuitive way of specifying information needs. For ex- ple, users should know that predicate “actedIn” means “starring in” ample, we input two keywords “Joanne Woodward” and “Golden and the Philadelphia film’s URI is “Philadelphia(film)”. In real ap- Globe Award” to discover unbounded relations (i.e., the paths in plications, it may not be practical to have full knowledge about the RDF graphs) between them. However, keyword search may return a larger number of non-informative search answers to users. In fact, users’ query intensions cannot be well modeled using a single query type in many real-life applications. Hence, a hybrid Permission to make digital or hard copies of all or part of this work for search capability is desired. In this paper, we propose an integrated personal or classroom use is granted without fee provided that copies are query formulation (called a SPARQL-Keyword query, shorted as not made or distributed for profit or commercial advantage and that copies SK query) and the solution framework by combining advantages of bear this notice and the full citation on the first page. To copy otherwise, to SPARQL and keyword search. Generally speaking, the results of republish, to post on servers or to redistribute to lists, requires prior specific SK query is the k SPARQL matches that are closet to all keywords permission and/or a fee. WOODSTOCK ’97 El Paso, Texas USA in RDF graph G, where k is a parameter given by users. The formal Copyright 20XX ACM X-XXXXX-XX-X/XX/XX ...$15.00. definition of SK query is given in Definition 2.2. Subject Predicate Object 001 002 003 004 "Academy Award Place type Philadelphia(place) label "Philadelphia" DenzelWashington type Actor for Best Actress" 009 DenzelWashington label "Denzel Washington" 007 label livesIn "Mogambo" DenzelWashington actedIn Philadelphia(film) "Grace Kelly" DenzelWashington wonPrize ActorAcademyAward 005 006 label ActressAcademyAward wonPrize GraceKelly 008 011 JoanneWoodward type Actor type Actor label JoanneWoodward label "Joanne Woodward" label 010 Film JoanneWoodward wonPrize ActressAcademyAward wonPrize actedIn 013 type JoanneWoodward wonPrize GoldenGlobeAward Award type 013 type GoldenGlobeAward Mogambo 014 JoanneWoodward actedIn Philadelphia(film) 012 wonPrize WorkingGirl GraceKelly type Actor "Joanne label wonPrize GraceKelly label "Grace Kelly" Woodward" 015 actedIn GraceKelly actedIn Mogambo wonPrize "Golden Globe Award 016 GraceKelly wonPrize ActressAcademyAward label for Best Actress" MelanieGriffith label GraceKelly wonPrize GoldenGlobeAward 017 008 type GraceKelly livesIn Philadelphia(place) JoanneWoodward type Actor 019 004 018 label AntonioBanderas type Actor Clear part of query requirement: Fuzzy partisMarriedTo of query requirement: "Working Girl" "Philadelphia" "Antonio Banderas" AntonioBanderas label "Antonio Banderas" actors acted actedInin Philadelphia typeAcademy Award, 022 AntonioBanderas actedIn Philadelphia(film) label label Golden Globe Award AntonioBanderas isMarriedTo MelanieGriffith 020 021 "Melanie Griffith" 024 011 Philadelphia(film) actedIn AntonioBanderas MelanieGriffith type Actor 023 Academy Award MelanieGriffith label "William Holden" type "Academy Award Film related to for Best Actor" MelanieGriffith wonPrize GoldenGlobeAward actedIn "Denzel Washington" MelanieGriffith actedIn WorkingGirl label label 008 025related 026 to 010 ActressAcademyAward type Award Golden Globe AwardAward ActressAcademyAward label "Academy Award for Best Actress" Actor type DenzelWashington wonPrize ActorAcademyAward type ActorAcademyAward type Award ActorAcademyAward label "Academy Award for Best Actor" (b) Example RDF Graph GoldenGlobeAward type Award GoldenGlobeAward label "Golden Globe Award for Best Actress" Philadelphia(film) type Film SPARQL: Keyword: Philadelphia(film) label "Philadelphia" Academy Award WorkingGirl type Film WorkingGirl label "Working Girl" ?f Actor Golden Globe Award Mogambo type Film label Mogambo label "Mogambo" actedIn type Philadelphia(place) type Place ?x Philadelphia(place) label "Philadelphia" Philadelphia
(a) Example RDF Triples (c) Example SPARQL-Keyword Query Figure 1: RDF Examples
Let us recall Example 1 again. We issue the following SK query 021 (AntonioBanderas) to 017 (JoanneWoodward). The first one is hQ, qi. The SPARQL query graph Q is given in Figure 1(c), while through 020 (Philadelphia(film)), while the second is through 008 the keywords are q = {Academy Award, Golden Globe Award}. (Actor). It is obvious that two people cooperating in the same film Figure 3 shows three different results. First, there are three different is more meaningful than both of them being actors, so the two-hops subgraph matches of query Q, i.e., M1, M2 and M3. Then, the path through 020 has more relation strengths than the two-hops keywords are matched in different literal vertices, i.e., 001, 015 path through 008. Therefore, following the intuition of TF-IDF for and 026. The distance between a subgraph match M and a keyword measuring the word importance in a corpus, we propose “predicate in q is the shortest distance between M and one vertex containing salience” (see Section 2) to evaluate relation strengths. keywords. We find that M1 is the closest to the two keywords. Another challenge of this problem is the search efficiency. A It says “Joanne Woodward starring in Philadelphia film won both naive “exhaustive-computing” strategy works as follows: we first Academy Award and Golden Globe Award”. Obviously, this is an find all subgraph matches of Q (in RDF graph G) by existing tech- informative answer to the query in Example 1. niques; then, we compute the shortest path distances between these subgraph matches and the vertices containing keywords on the fly; SPARQL related to Keywords finally, the matches with shortest distances to keywords are re- 020 008 005 001 Philadelphia(film) Actor "Academy Award for ActressAcademyAward label turned as answers. Obviously, this is an inefficient solution. Given Best Actress" label actedIn type wonPrize a SPARQL query Q, there may exist some matches of Q that are 004 017 013 015 "Golden Globe Award Philadelphia JoanneWoodward wonPrize GoldenGlobeAward label for Best Actress" far from the keywords in RDF graphs. These matches cannot con- M1 tribute to the final results. Therefore, it is unnecessary to identify all 017 JoanneWoodward 015 020 directed subgraph matches in RDF graph. Instead of the exhaustive comput- Philadelphia(film) "Golden Globe Award 008 wonPrize 013 Actor label for Best Actress" ing, we only find matches of SPARQL query Q progressively and GoldenGlobeAward label actedIn 004 type 026 025 013 design a lower bound that stops the search process as early as pos- Philadelphia "Academy Award for DenzelWashington wonPrize GoldenGlobeAward label Best Actor" sible. Moreover, we propose a star index to enable the structural M2 005 pruning. ActressAcademyAward 015 020 label In summary, we made the following contributions in this paper. Philadelphia(film) wonPrize "Golden Globe Award actedIn 017 JoanneWoodward for Best Actress" actedIn label 021 013 1. We propose a new query paradigm over RDF data combining 004 AntonioBanderas GoldenGlobeAward 001 Philadelphia label keywords and SPARQL(called an SK query), and design a type isMarriedTo 016 wonPrize "Academy Award for 008 Actor MelanieGriffith Best Actress" novel solution for this problem.
M3 Figure 3: SK Query Results 2. We design an index to speed up SK query processing. We propose a frequent star pattern-based index to reduce the search In the above analysis, we assume that the relation strength de- space. pends on the path length, i.e., the number of hops. Actually, dif- ferent predicates should have different weights to evaluate the re- 3. We evaluate the effectiveness and efficiency of our method lation strength. For example, there are two two-hops paths from in real large RDF graphs and conclude that our methods are much better than comparative models in both effectiveness DEFINITION 2.5. Given a result hM, {v1, v2, ..., vn}i for an SK (in terms of NDCG@k) and query response time. query hQ, qi, the distance between match M and vertex vi (i = 1, ..., n) is defined as follows. The remainder of this paper is organized as follows: Section 2 d(M, v ) = MIN {d(v, v )} defines the preliminary concepts. Section 3 gives an overview of i v∈M i our approach. We introduce a structural index to efficiently find where v is a matching vertex in M with regard to a variable in the candidates of variables in SPARQL queries in Section 4. We SPARQL query Q and d(v, vi) is the shortest path distance between discuss how to compute the results of SK queries in Section 5. Ex- v and vi in RDF graph G. perimental results are presented in Section 6. Related works and Then, the structure cost of a result r = hM, {v1, v2, ..., vn}i is de- the final conclusion are drawn in Section 7 and 8, respectively. fined as follows.
Xi=n 2. BACKGROUND Coststructure(r) = d(M, vi) i=1 In this section, we introduce the fundamental definitions used in this paper. (Problem Definition) Given an SK query hQ, qi and a parameter 2.1 Preliminaries k, our problem is to find k results (Definition 2.2), which have the k-smallest costs. An RDF dataset consists of a number of triples, which is corre- sponding to an RDF graph. The SK query is to find k SPARQL 2.2 Predicate Salience matches that are top-k nearest with regard to all keywords. In this paper, we use “shortest path distance” to evaluate the re- lation strength. However, the naive definition of the shortest path DEFINITION 2.1. An RDF data graph G is denoted as hV(G), E(G), distance suffers from a critical problem: all predicates, i.e., edge Li, where (1) V(G) = VL ∪ VE ∪ VC is the set of vertices in RDF labels, are considered equally important when it is used to measure graph G, where VL, VE and VC denote literal vertices, entity ver- the relationship strength between entities. In fact some predicates tices and class vertices, respectively; (2) E(G) is the set of edges in have little or no discriminating power in determining relevance. For G; and (3) L is a finite set of edge labels, i.e. predicates. example, predicates like ”type” and “label” are so common that each entity is incident to a class vertex through an edge of predicate DEFINITION 2.2. A SK (SPARQL & Keyword) query is a pair “type”. This tends to incorrectly emphasize paths which contain hQ, qi, where Q is a SPARQL query graph and q is a set of keywords these common predicates more frequently, without giving enough {w1, w2, ..., wn}. weight to the paths of more meaningful predicates (like “actedIn” Given an SK query hQ, qi, the result of hQ, qi in a data graph G and “isMarriedTo”). The predicates like ”type” and “label” are not is a pair hM, {v1, v2, ..., vn}i, where M is a subgraph match of Q in good predicates to distinguish relevant and non-relevant vertices, G and vi (i = 1, ..., n) is a literal vertex (in G) containing keyword unlike the less common predicates “actedIn” and “isMarriedTo”. wi. Hence, we should introduce a mechanism for attenuating the ef- fect of predicates that occur too frequently in the RDF graph to be Given an SK query hQ, q = {w1, ..., wn}i, the cost of a result r = meaningful for relevance determination. Learning from the con- hM, {v1, v2, ..., vn}i contains two parts. The first part is the content cept of document frequency, we first find out the set of vertices in cost and the second part is the structure cost. the RDF graph incident to a predicate p, which is denoted as V(p). Then, we divide the size of V(p) by the total number of vertices. DEFINITION 2.3. Given a result r = hM, {v1, v2, ..., vn}i, the cost We name the measure as the predicate salience of predicate p and of r is defined as follows: give the formal definition as follows: |V(p)| Cost(r) = Costcontent(r) + Coststructure(r) ps(p) = , |V(G)| where Costcontent(r) is the content cost of r (defined in Definition Thus the predicate salience of a rare predicate is low, whereas the 2.4) and Coststructure(r) is the structure cost of r (defined in Defini- tion 2.5). predicate salience of a frequent predicate is likely to be high, which means that rare predicates have less cost than frequent predicates. Let us consider RDF graph in Figure 1(b). The predicate salience DEFINITION 2.4. Given a result r = hM, {v1, v2, ..., vn}i, the con- values of all predicates are given in Table 1.As shown in Table 1, tent cost of r = hM, {v1, v2, ..., vn}i is defined as follows: predicate “actedIn” is more important than “type” in measuring the Xi=n relation strength, while the former’s predicate salience is 0.296 and Costcontent(r) = C(vi, wi) i=1 the latter’s is 0.593. where C(vi, wi) is the matching cost between vi and keyword wi. Predicate Predicate Salience actedIn 0.296 Any typographic or linguistic distances, such as string edit dis- isMarriedTo 0.074 tances [31] and google similarity distance [7], can be used to mea- label 0.852 livesIn 0.074 sure C(vi, wi). In applications, users are more interested in some variables (in type 0.593 wonPrize 0.259 SPARQL query Q) than the constants in Q. Let us recall Exam- ple 1. The distance between keywords and the matching vertices Table 1: Weights of Predicates in Example RDF Graph with regard to variable “?a” is more interesting to measure the re- lationship strength. Therefore, to evaluate the structure cost (in 3. OVERVIEW Definition 2.5), we only consider the matching vertices with regard In this section, we give an overview of the different steps in- to variables in SPARQL query Q. volved in our process of SK query, which is depicted in Figure 4. In this paper, we are concerned with the challenge of efficiently Data PreprocessingIn this section, we first introduce an structural index based on finding the results of SK queries. We propose an approach in which a certain kind of patterns in Section 4.1. Then, we discuss how the best results of the SK query are computed using the graph ex- to generate the candidate lists of variables based on our structural Query Computation ploration. We detail the different steps of the approach below. index 4.2. 4.1 Structural Index Keyword Mapping Keywords Keyword Vertices Top-k Results Top-k Results of In this section, we propose a frequent star pattern-based index. Candidate Generation Computation SK Queries We mine some frequent star patterns in G. For each frequent star SPARQL SPARQL Candidates S , we build an inverted list L(S ) that includes all vertices (in RDF Keyword Index Structural Index graph G) contained by at least one match of S . A reason for select- (Inverted Index) ing stars as index elements is that SPARQL queries tend to contain star-shaped subqueries, for combining several attribute-like proper- Frequent Star Patterns ties of the same entity [22].
RDF Data Graph We propose a sequential pattern mining-based method to find frequent star patterns in RDF graphs. For each entity vertex in an Figure 4: Overview of Our Approach RDF graph, we sort all its adjacent edges in lexicographic order Keyword Mapping. In the offline phase, we create an inverted of edge labels (i.e. properties). These sorted edges can form a index storing a map from keywords to its locations in the RDF sequence. For example, vertex “Philadelphia(film)” has five adja- graph. In the online phase, we map keywords to vertices based cent edges, that are hactedIn, actedIn, actedIn, name, typei. Ta- on the inverted index. ble 2 shows a sequence database, where each sequence is formed For scoring keyword vertices, a widely used metric that is com- by the adjacent edges of one entity vertex. We employ the exist- puted on-the-fly for a given query is IR-style TF/IDF cost. Many ing sequential pattern mining algorithms, such as PrefixSpan[24], cost functions have been proposed in the literature, and we select to find frequent sequential patterns, where each sequential pattern one of them to assign the cost to each vertex containing keywords. corresponds to a star pattern in RDF graphs. For example, as- Note that we need to normalize the cost of keyword matching ver- sume that the minimal support count s = 2, hactedIn, typei and tices before the distances computation. hactedIn, type, wonPrizei are two frequent sequential patterns. It In this paper, our primary focus is indexing and query process- is easy to know that a sequential pattern always corresponds to one ing, so we will not delve into the specifics of keyword mapping. star pattern, as shown in Figure 5. For ease of presentation, we use Candidate Generation. When we find a vertex reachable to ele- the terms “sequential patterns” and “star patterns” interchangeably ments of all keywords, we need to run subgraph homomorphism to in the following discussion. check whether there exist some subgraph matches (of Q) contain- Vertex Predicate Sequence ing v. As we know, subgraph homomorphism is not efficient due Philadelphia(film) hactedIn, actedIn, actedIn, label, typei to its high complexity [14]. In order to speed up query process- JoanneWoodward hactedIn, actedIn, label, type, wonPrizei ing, we propose a filter-and-refine strategy to reduce the number of AntonioBanderas hactedIn, label, type, wonPrize, wonPrizei subgraph homomorphism operations. The basic idea is to filter out ...... some vertices that are not in any subgraph match of Q. We call them “dummy” vertices. If the search meets a dummy vertex, we Table 2: Example of Predicate Sequences do not perform subgraph homomorphism algorithm. star pattern sequential pattern In this paper, we propose a frequent star pattern-based structural
Assume that (v, p, |p|) is popped from queue PQi. For each inci- state as follows. dent edge vv0 to v, we obtain a new element (v0, p∪vv0, |p|+ps(vv0)), where p ∪ vv0 means appending an edge to p and ps(vv0) denotes DEFINITION 5.4. Given a SPARQL query graph Q with m ver- 0 0 <020,022,030,−> the predicate salience value of the edge label of vv . If pi ∪ vv tices u1, ..., um, a state is a (partial) match of query graph Q. is not a simple path1, the element is ignored (Line 8-9 in Algo- rithm 1). Then, we check whether there exists another element For example, Figure 6 shows an example state of the SPARQL (v0, p0, |p0|) that has the identical vertex v0 with the new element query in Figure 1(c). (v0, p ∪ vv0, |p| + ps(vv0)), where |p0| > |p| + ps(vv0)). If so, we 0 0 0 0 0 0 020 008 delete (v , p , |p |) from PQi and insert (v , p ∪ vv , |p| + ps(vv )) ?f Actor Philadelphia(film) Actor into PQi (Line 12-13 in Algorithm 1). Otherwise, we ignore the label actedIn type actedIn type new element (Line 15 in Algorithm 1). If there exists no element 017 (v, p0, |p0|), we insert (v0, p∪vv0, |p|+ps(vv0)) into the queue directly Philadelphia ?x JoanneWoodward (Line 17 in Algorithm 1). (a) Query Graph (b) State
DEFINITION 5.3. Fully-seen Vertex, Partially-seen Vertex and Figure 6: A State Matching a Part of Q Un-seen Vertex. Given a vertex v, if v is seen by all keywords wi In particular, our state transformation algorithm is as follows. (i = 1, ..., n), v is called a fully-seen vertex; if v is not a fully-seen Assume that
030 020 030 020 020 022 Actor Philadelphia(film) Actor Philadelphia(film) Actor JoanneWoodward actedIn type label actedIn type 022 type 022 021 022 JoanneWoodward JoanneWoodward Philadelphia JoanneWoodward
Vertex "017" is a fully-seen vertex, so we ignore this search branch
020 Philadelphia(film)
label actedIn 004 017 020 "Philadelphia" JoanneWoodward Philadelphia(film) 020 label Philadelphia(film) 004 "Philadelphia" 020 020 008 Philadelphia(film) Philadelphia(film) Actor
label actedIn label actedIn type 004 021 004 021 "Philadelphia" AntonioBanderas "Philadelphia" AntonioBanderas
Match M2 Figure 7: Finding Matches Containing Vertex “020” by Pruning the Search Branch Beginning from “017” all matches containing v has been found if any. When we search the RDF graph beginning with a fully-seen vertex, if the search Fully-seen Match Un-seen Match meets another fully-seen vertex v00, it can skip v00 (Line 15 - 16 in Algorithm 2). This is because that the matches containing v00 have been found before. Partially-seen Match EXAMPLE 2. We assume that the current popped fully-seen ver- keywords tex is “020” and vertex “017” is another a fully-seen vertex. As shown in Figure 7, we explore the RDF graph from “020” to “017”. However, vertex “017” is a fully-seen vertex, so all SPARQL matches containing “017” have been found already. As a result, we can ter- minate the corresponding search branches in Figure 7. All Vertices in RDF Graph Fully-seen Vertex 5.3 Top-k Computation Partially-seen Vertex or Un-seen Vertex The native solution for computing top-k results of a SK query Figure 8: Fully-seen Match, Partially-seen Match and Un-seen is to run the backward search algorithm until that all vertices (in Match during the Backward Search RDF graph G) have been fully-seen by keywords. Then, according to the results’ cost, we can find the top-k results. Obviously, this is an inefficient solution especially when G is very large. In this Fully-seen Match. For a fully-seen match, we compute its match subsection, we design an early-stop strategy. cost according to Definition 2.5. If we have found more than k Let us consider a snapshot of some iteration step in Algorithm fully-seen matches, we maintain a threshold δ be the k-th smallest 1. All subgraph matches of SPARQL query Q can be divided into match cost. three categories: fully-seen matches, partially-seen matches and Partially-seen Match. For any partially-seen match, we com- un-seen matches. pute the lower bound of its cost as follows. DEFINITION 5.5. Fully-seen Match, Partially-seen Match and THEOREM 5.2. Given a partially-seen match M of SPARQL Un-seen Match. Given a subgraph match M of SPARQL query Q, query Q, v is a partially-seen vertex or an un-seen vertex in the if all vertices in M are fully-seen vertices, M is called a fully-seen match. The following equation holds. match; if M is not a fully-seen match and M contains at least one Cost(M) = P d(v, w ) fully-seen vertex, it is called a partially-seen match. If a match i P 1≤i≤n P M does not contain any fully-seen vertex, it is called an un-seen ≥ d[v][wi] + |pi| match. d[v][wi],null∧1≤i≤n d[v][wi]=null∧1≤i≤n
where d[v][wi] is the i-th dimension of v’s vector correspond- Figure 8 demonstrates a visual representation of three kinds of ing to keyword wi, and |pi| corresponds to the current queue head matches. The shaded area covered by the dash line circle denotes (v, pi, |pi|) in queue PQi. all fully-seen vertices in RDF graph. With the increasing of the iteration steps (in Algorithm 1), the shaded area expands gradually PROOF. If d[v][i] , null, it means that we have computed out until that it covers the whole RDF graph. The early-stop strategy d(v, wi). If d[v][wi] = null, v has still not been seen. Since each is to stop the expansion as early as possible, but we can guarantee time we pop the head (v, pi, |pi|) of PQi where |pi| is the smallest, that we have found the top-k results for SK queries. all un-seen vertices’ distances to wi are larger than |pi|. The basic idea of our early-stop strategy is as follows. We only According to Theorem 5.2, we define the lower bound of a partially- compute the cost of fully-seen matches. Then, we use the fully- seen match M as follows. seen matches to find a threshold δ, which is the k-th smallest cost so far. If there are less than k fully-seen matches so far, δ is ∞. We DEFINITION 5.6. Given a match of SPARQL query Q, the lower compute the lower bounds θ1 and θ2 for partially-seen matches and bound for a partially-seen match M is defined as follows. un-seen matches, respectively. The algorithm can early stop if and X X only if δ < θ ∧ δ < θ . Otherwise, the algorithm continues the next lb(M) = MIN( d[v][wi] + |pi|) 1 2 v∈M iteration. d[v][wi],null∧1≤i≤n d[v][wi]=null∧1≤i≤n The lower bound for all partially-seen matches is defined as fol- For efficiency study, because there are no existing method for lows. SK queries, we evaluate our approach with two baselines, i.e., the exhaustive computing and the naive backward search and . “Ex- DEFINITION 5.7. The lower bound θ1 for all partially-seen matches haustive computing” has been introduced in Section 1. The naive is as follows. backward search is to run the backward search algorithm until that all vertices have been fully-seen by keywords. Then, according to θ1 = MINM∈PS (lb(M)) the results’ cost, we find the top-k results. where PS denotes all partially-seen matches and lb(M) is defined Our experiments are conduct on a machine with 2 Ghz Core 2 in Definition 5.6. Duo processor, 16G RAM memory and running Windows Server 2008. All experiments are implemented in Java languages. We use With the increasing of the iteration steps, some partially-seen MySQL to store the RDF graphs and the indices. matches become fully-seen matches. They are moved to FS . The threshold δ and θ1 are updated accordingly. 6.1 Datasets & Setup Un-seen Match. Let us consider an un-seen match M. There are We use three real-world RDF datasets, DBLP, Yago and DBPe- two kinds of vertices in M, i.e., partially-seen vertices and un-seen dia in our experiments. The details about the two datasets are as vertices. follows. THEOREM 5.3. For an un-seen vertex v, if threshold δ , ∞, the DBLP. DBLP 2 contains bibliographic information of computer following equation holds. science publications [21]. The DBLP graph contains 8, 381, 858 X RDF triples and 3, 103, 614 vertices. We define 5 sample SK queries ≤ δ d(v, wi) for DBLP and show two of them in Table 3 for case study. 1≤i≤n Yago. Yago3 extracts facts from Wikipedia and integrates them PROOF. For each keyword wi, we assume that the queue head with the WordNet thesaurus [27]. The RDF graph has 19, 012, 849 of PQi is (v, pi, |pi|). Since v is an un-seen vertex, |pi| ≤ d(v, wi) edges and 12, 811, 222 vertices. We define 8 sample SK queries for for each keyword wi. In contrast, δ is the upper bound of the top- Yago and show two of them for case study in Table 4. k results, so δ is equal to the cost of a fully-seen match M. Each DBPedia & QALD. DBPedia 4 is an RDF dataset extracted from 0 0 vertex v in M is fully-seen vertex. Hence, d(v , wi) ≤ |pi|. Then, Wikipedia. The DBPedia contains 73, 766, 900 edges and 13, 100, 739 we know that d(v0, w ) ≤ |p | ≤ d(v, w ) for each keyword w . In 5 P i i i i vertices. QALD is an evaluation campaign on question answer- conclusion, δ ≤ d(v, wi). ing over linked data. It is co-located with the ESWC 2012. In 1≤i≤n this campaign, the committee provides some questions and each According to Theorem 5.3, it is not necessary to consider un- question is annotated with some recommended keywords and the seen vertices to define the lower bound for un-seen matches. There- answers that these queries retrieve. Note that, some questions in fore, we define the lower bound for all un-seen matches as follows. QALD are so simple that they can map to a SPARQL query with only one edge. These simple questions are unnecessary to be split DEFINITION 5.8. The lower bound θ2 for all un-seen matches into a SPARQL query and some keywords. Thus, we only select 10 is as follows. non-aggregation complex queries from QALD for evaluation. Two X X of them are as shown in Table 5 for case study. θ2 = MIN( d[v][wi] + |pi|) v∈PS et All sample queries are shown in Appendix. d[v][wi],null∧1≤i≤n d[v][wi]=null∧1≤i≤n where PS et contains all partially-seen vertices so far, d[v][wi] is 6.2 Effectiveness Study the i-th dimension of the v’s vector corresponding to keyword wi In this section, we compare our method with a classical key- and |pi| corresponds to the current queue head (v, pi, |pi|) in queue word search algorithm BANKS [2] over DBLP and Yago to show PQi. the effectiveness of our method. Furthermore, since each resource in DBPedia is annotated by Wikipedia documents, so we design a Early-stop Strategy . In each iteration step, we check whether stronger baseline named as “Annotated SPARQL” for DBPedia. δ ≤ θ1 ∧δ ≤ θ2. If the condition holds, the algorithm can stop, since any partially-seen match or un-seen match cannot be in one of the 6.2.1 Case Study top-k results. We show six sample queries in Table 3, 4 and 5 for the case study. 6. EXPERIMENTS DBLP. Let us consider the two sample queries in DBLP. The In this section, we evaluate our approach in three large real RDF top-3 results answered by the SK query and BANKS over DBLP graphs, DBLP, Yago and DBPedia. are shown in Table 6. For effectiveness study, we compare our method with a classical Q3: Which researchers on keyword search published papers in keyword search algorithm BANKS [2] over both Yago and DBPe- VLDB 2004 and DEXA 2005? dia. Furthermore, since each resource in DBPedia is annotated by The three results returned in SK query are three researchers named Wikipedia documents, so we design a stronger baseline named as “Kesheng Wu”, “Jeffrey Xu Yu” and “Maurice van Keulen”. All “Annotated SPARQL” for DBPedia. “Annotated SPARQL” is sim- of them published paper in both VLDB 2004 and DEXA 2005. As ilar to the approach discussed in [33]. It first finds out all matches well, they wrote papers about keyword search before. However, the of the SPARQL query, then ranks these matches by how closely first three results returned by traditional keyword search are “Kat- the corresponding Wikipedia documents match the keywords. Note sumi Tanaka”, “Mong-Li Lee” and “Reda Alhajj”. Although all that, except for DBpedia, most current RDF datasets do not provide 2http://sw.de ri.org/ aharth/2004/07/dblp/ such documents to annotate the resources. Hence, we only do ex- 3http: //www.mpi-inf.mpg.de/yago-naga/yago/ periments of annotated SPARQL over DBPedia. For other RDF 4http://downloads.dbpedia.org/3.7/en/ datasets, although we can crawl some pages to annotate their enti- 5http://greententacle.techfak.uni-bielefeld.de/∼cunger/qald/index.php?x ties, that is beyond the scope of this paper. =challenge&q=2 SK Query SK Query Query Sematic SPAQRL Keywords Query Sematic SPAQRL Keywords Select ?person where { Which states of Germany Select ?s where { Social Demo- ?paper year 2004; Q are governed by the Social ?s country ?g; Which researchers on key- 3 cratic Party ?paper booktitle VLDB; Democratic Party? ?g name “Germany”;} word search published pa- keyword Q3 ?paper1 year 2005; Select ?u where { pers in VLDB 2004 and search Which monarchs of the United King- ?paper1 booktitle DEXA; ?u spouse ?s; DEXA 2005? Q United Kingdom were dom, ?paper1 creator ?person; 4 ?s birthPlace ?c; married to a German? monarch ?paper dc:creator ?person;} ?c name “Germany”;} Select ?paper where { Which papers in KDD ?paper year 2003; Table 5: Sample QALD Queries over DBPedia for Case Study 2005 about concept- concept- Q4 paper booktitle KDD; drifting are written by drifting ?paper creator ?person; Top-3 Results of SK Query Top-3 Results of BANKS Jiawei Han? ?person name Jiawei Han;} Kesheng Wu Katsumi Tanaka Q3 Jeffrey Xu Yu Mong-Li Lee Maurice van Keulen Reda Alhajj On Reducing Classifier Granularity Table 3: Sample DBLP Queries for Case Study Mining concept-drifting data in Mining Concept-Drifting streams using ensemble classifiers Data Streams. SK Query CLOSET+: searching for ACE: Adaptive Classifiers-Ensemble Query Sematic SPAQRL Keywords Q4 the best strategies for mining System for Concept-Drifting Which actors/actresses Academy Select ?p where{ frequent closed itemsets. Environments. played in Philadelphia are Award, ?p type actor; CloseGraph: mining closed Q mostly related to Academy Golden Baile Shi 1 ?p actedIn ?f; frequent graph patterns. Award and Golden Globe Globe ?f label “Philadelphia”; } Award? Award Which Turing Award Select ?p where { winners in the field of ?p type scientist; Toronto, Table 6: Effectiveness Results for Sample DBLP Queries Q 2 database are mostly ?p hasWonPrize ?a; database related to Toronto? ?a label “Turing Award”;} rithm. The third one is “Kenneth E. Iverson”. Prof. Kenneth E. Table 4: Sample Yago Queries for Case Study Iverson also received the Turing Award. He was died in Toronto. In contrast, the first two results returned by traditional keyword search are “English Language” and “Princeton University”. Obvi- of them are interested in keyword search, none of them published ously, they are non-informative results. Here, keywords for key- paper in VLDB 2004. word search that we use are {Turing Award, winners, Toronto}. Q : Which papers in KDD 2005 about concept-drifting are writ- 4 Top-3 Results of SK Query Top-3 Results of BANKS ten by Jiawei Han? The first result returned in SK query is a paper named“Mining Denzel Washington Grace Kelly Q Joanne Woodward George Cukor concept-drifting data streams using ensemble classifiers”. This pa- 1 Antonio Banderas Joanne Woodward per was written by Jiawei Han and published in KDD 2005. This Stephen Cook English language is a paper closely related to concept-drifting. This is the best an- Q2 William Kahan Princeton University swer to query Q2. The other two results of SK queries are still two Kenneth E. Iverson Turing Award paper written by Jiawei Han and published in KDD 2005. In con- Table 7: Effectiveness Results for Sample Yago Queries trast, the first two results returned by traditional keyword search are two papers about concept-drifting, but none of them was published DBPedia & QALD. Let us consider the two sample QALD queries in KDD 2005 or written by Jiawei Han. The third result of tradi- over DBPedia. The top-3 results answered by BANKS, the SK tional keyword search is a researcher, which is more unrelated to query and “Annotated SPARQL” over DBPedia are shown in Table the query. 8. Yago. Let us consider the two sample queries in Yago. The top- Top-3 Results of Top-3 Results of Top-3 Results of 3 results answered by the SK query and BANKS over Yago are SK Query BANKS Annotated SPARQL shown in Table 7. Hanau Australia Hans-Ulrich Rudel Q1: Which actors/actresses played in Philadelphia are mostly Q3 Hanhofen Bombardier Transportation Hans Dauser related to Academy Award and Golden Globe Award? Hanover Canada Hans Heidtmann We have analyzed query Q1 in Section 1. For comparison, we William IV of 2004 Amsterdam William IV of use keywords {actors, actresses, Philadelphia, Academy Award, the United Kingdom Admirals season the United Kingdom Golden Globe Award} for keyword search. Generally, SK query re- Carl XVI Gustaf of 2004 Berlin Beatrix of Q4 turns more reasonable answers than the traditional keyword search. Sweden Thunder season the Netherlands Beatrix of 2004 Cologne Switzerland In contrast, the first two results returned traditional keyword search the Netherlands Centurions season are “Grace Kelly” and “George Cukor”. Grace Kelly lived in Philadel- phia, and George Cukor is also an actor that directed the film, The Table 8: Effectiveness Results over DBPedia for Sample QALD Philadelphia Story, in 1940. Queries Q2: Which Turing Award winners are mostly related to Toronto? The first result returned in SK query is “Stephen Cook”. As we Q3: Which states of Germany are governed by the Social Demo- know, Stephen Cook is a professor in University of Toronto. He cratic Party? won the Turing award for his contributions to complexity theory. The first three results returned in SK query are three places in This is the best answer to query Q2. The second answer is “William Germany and governed by the Social Democratic Party. However, Kahan”. Prof. William Kahan was born in Toronto and won the the first three results returned in annotated SPARQL are three mem- Turing award for his contributions to the numerical analysis algo- bers of the Social Democratic Party in Germany. The first three re- NDCG@3 NDCG@5 NDCG@10 6.3.1 Offline Performance Yago BANKS 0.3455 0.39 0.4643 SK query 0.815 0.868 0.872 We report the index size and index construction time in Table DBLP BANKS 0.7143 0.684 0.685 14. Since our structural index is based on the efficient sequential SK query 0.93 0.8867 0.8738 pattern mining, we can finish the structural index construction in several minutes. Table 9: Average NDCG Values Index Construction Time(s) Index Size(MB) DBLP 77.885 377.977 sults returned by traditional keyword search are three place far from Yago 176.67 844.066 Germany. Hence, the results of SK queries are more informative DBPedia 600.263 283.559 than the other two methods. Here, keywords for keyword search Table 14: Index Size and Index Construction time are {state, Germany, govern, S ocialDemocraticParty}, which are given in QALD. 6.3.2 Pruning Effect of Structural Index Q4: Which monarchs of the United Kingdom were married to a Based on the indices introduced in Section 4, we can avoid many German? times to call Algorithm 2 for graph matching by pruning many un- The first result of both SK query and annotated SPARQL are satisfied vertices. Moreover, the vertices which are too far to be in William IV of the United Kingdom, which is the best answer. The a final answer can be safely pruned. In this experiment, we report other two results of SK query are still two royals in Europe. How- the pruning efficiency of our structural index. We make a compari- ever, the third result of annotated SPARQL is a European nation. son of the number of graph matching operations that the advanced In addition, the first three results returned by traditional keyword backward search accessed and the number of graph matching oper- search are non-informative results. Here, keywords for keyword ations that the naive backward search accessed. search are {United Kingdom, monarch, married, German}, which Tables 11, 12 and 13 show the number of graph matching opera- are also given in QALD. tions on DBLP, Yago and DBPedia. The number of graph matching 6.2.2 NDCG@k over Yago and DBLP operations in advanced backward search is not less than the basic backward search. In most case, we avoid a large number number In order to quantify the effectiveness of SK query, we evaluate of graph matching operations. the NDCG (Normalized Discounted Cumulative Gain [16]) of both SK query and the keyword search. Since there are no golden stan- 6.3.3 Online Performance dards, we invite 10 volunteers to judge the result quality. Specif- In this section, we evaluate the efficiency of our method. Figure ically, we ask each volunteer to rate the goodness of the results 9 shows the time cost of the three methods. returned by SK query and the keyword search method. The score As shown in Figure 9, our method outperforms the baseline method is between 1 and 5. Higher the score, better the result. by 2 or more times in most case. Especially for Q3 on Yago and Table 9 reports NDCG@k values by varying k from 3 to 10 in Q2, Q5 on DBLP, our method only takes a fifth of the exhaustive- both Yago and DBLP. SK query outperforms the traditional key- computing. This is because that the matches of these SPARQLs are word search by 20%-50%. Furthermore, we find that the gap in close to vertices containing keywords. Thus, the query processing Yago is larger than that in DBLP. The reason is that Yago has more can terminate soon. complex schema than DBLP. Thus, keywords may result in more Note that, because our inverted index for keywords are stored in ambiguity in Yago than in DBLP. It means that the superiority of disk, keywords mapping will cost much time and takes up a large SK query is more pronounced in semantic-rich data. part of the total time. Hence, it is difficult for our method to im- 6.2.3 MAP over DBPedia prove the efficiency too much. Since QALD provides the standard answers of each queries, we evaluate the MAP (Mean Average Precision [30]) to compare the 7. RELATED WORK SK query with BANKS and “Annotated SPARQL”. For SPARQL query, there have been many works to study it, such as [35, 1, 22, 23, 41, 5, 38]. Some of them [1, 5] store the RDF BANKS Annotated SPARQL SK query triples into RDBMS and answer the SPARQL via join operations. MAP 0.012 0.192 0.205 RDF-3x [22, 23] and Hexastore [35] create indexes for each permu- Table 10: MAP Value over DBPedia & QALD tation of subject, predicate and object. Since an RDF dataset can also be modeled as a graph, Trinity.RDF [38] and gStore [41] deem Table 10 reports MAP values of our ten QALD queries. Both SK answer the SPARQL in an RDF dataset as finding the subgraph query and annotated SPARQL outperforms the traditional keyword matches over an RDF graph. Trinity.RDF and gStore design a sub- search by a order of magnitude. The MAP value of the “annotated graph match algorithm similar to VF2 [8] to answer the SPARQL SPARQL” is smaller than the SK query. This is because that the query. VF2 [8] is an early efforts for subgraph isomorphism check. “annotated SPARQL” can do well when the documents associated VF2 starts with a vertex and explore to a vertex connected from the with the matches contains the keywords. In other words, the “an- already matched query vertices one by one. notated SPARQL” can work, only when the relation between the For keyword search, existing keyword search techniques over matches and the keywords is explicit. However, in pracitce, the RDF graphs can be classified into the following two categories. relation between the matches and the keywords is often implicit. The first kind of methods [34, 29, 12, 13] interpret keywords as Then, the SK query do better. SPARQL queries, and then retrieve results by involving existing SPARQL query engines. Another kind of methods aim to find 6.3 Efficiency Study the small-size substructures (in RDF graphs) that contains all key- In this section, we evaluate the efficiency of SK query in large words. The top-k substructures, such as trees [2, 17, 15, 10, 19, 20, real graphs. Here, the default number of returned results is set to 32], cliques [18], computed on the basis of a scoring function are be 10. returned to users. Q1 Q2 Q3 Q4 Q5 Naive Backward Search 292268 21885 254674 872426 2747 Our Approach 354 5 1684 669 1548 Table 11: The Number of Graph Matching Operations on DBLP
Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Naive Backward Search 600283 563736 301 167958 231210 271929 94012 254848 Our Approach 6 55 269 5414 32 9 292 15 Table 12: The Number of Graph Matching Operations on Yago
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0.2 0.2 1 Query Response Time (in ms) Query Response Time (in ms) 0 0 Query Response Time (in ms) 0 Q1 Q2 Q3 Q4 Q5 Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q Q Q Q Q Q Q Q Q Q Queries Queries 1 2 3 4 Queries5 6 7 8 9 10 (a) DBLP (b) Yago (c) DBPedia Figure 9: Online Performance
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APPENDIX A. QUERIES IN EXPERIMENTS Table 15 shows all of our sample queries over Yago and DBLP. Here, since our institution is in China, most volunteers that we in- vite are Chinese. Hence, some sample queries are about China. For more reasonable experiments, so we also sample 10 non- SK Query Query Sematic SPAQRL Keywords Select ?person where { ?paper year 2004 ?paper booktitle VLDB Which researchers on keyword search published papers in Q1 ?paper1 year 2005 keyword search VLDB 2004 and DEXA 2005? ?paper1 booktitle DEXA ?paper1 creator ?person ?paper creator ?person} Select ?paper where { ?paper year 2003 Which papers in KDD 2005 about concept-drifting are written Q2 paper booktitle KDD concept-drifting by Jiawei Han? ?paper creator ?person ?person name Jiawei Han} Select ?person1 where { ?paper year 2005; Who wrote a paper in ICDM 2005 with others and knew DBLP Q3 ?paper booktitle “ICDM”; Tamer Tamer? ?paper creator ?person1; ?paper dc:creator ?person2} Select ?person2 where { Who wrote a paper VLDB 2005 and kept a good relationship ?paper year “2005”; Jian Pei, Q4 to Jian Pei and Wen Jin? ?paper booktitle “VLDB”; Wen Jin ?paper creator ?person2;} Select ?person1, ?person2 where { ?paper year “2005”; Which two researchers did research about skyline and coau- Q5 ?paper booktitle “VLDB”; Skyline thored a paper in VLDB 2005? ?paper dc:creator ?person1; ?paper dc:creator ?person2} Select ?p where{ Which actresses played in Philadelphia are mostly related to ?p type actor; Academy Award, Q1 Academy Award and Golden Globe Award? ?p actedIn ?f; Golden Globe Award ?f label “Philadelphia”; } Select ?p where { Which Turing Award winners in the field of database are ?p type scientist; Toronto, Q2 mostly related to Toronto? ?p hasWonPrize ?a; database ?a label “Turing Award”;} Select ?c where { ?c type company; Q3 Which Microsoft ˛ars´ products are about SDK? SDK ?c label “Microosft”; ?c created ?s;} Select ?p where { ?p actedIn ?f1; Which English film producers did act in a Comedy film and Q4 ?p y:created ?f2; Peking University relate to Peking University? ?f1 type ComedyFilms; ?f2 y:hasProductionLanguage English;} Select ?p where { Which top members of Communist Party of China are related ?p isAffiliatedTo ?u; Yago Q5 Kissinger Kissinger? ?u label “Communist Party of China”; ?p type Politician;} Select ?p1 where { Whose father was United States Army generals and took part Q6 ?p hasChild ?p1; Normandy Invasion in Normandy Invasion? ?p type UnitedStatesArmyGenerals ;} Select ?p where { Which state generated a Los Angeles Lakers player that relate ?p bornIn ?c; Q7 Eagle Colorado to Eagle, Colorado? ?c locatedIn ?s; ?p type LosAngelesLakersPlayers;} Select ?p where { Which participants of People’s National Congress did graduate Q8 ?p graduatedFrom ?u; People’s National Congress from universities in Beijing? ?u type UniversitiesInBeijing;}
Table 15: Sample Queries over Yago and DBLP SK Query Query Sematic SPAQRL Keywords Select ?s where { Which states of Germany are governed by the Social Q1 ?s country ?g; Social Democratic Party Democratic Party? ?g name “Germany”;} Select ?u where { Which monarchs of the United Kingdom were married to ?u spouse ?s; United Kingdom, Q2 a German? ?s birthPlace ?c; monarch ?c name “Germany”;} Select ?u where { Which capitals in Europe were host cities of the summer Olympic games, Q3 ?s type Country; olympic games? Europe ?s capital ?u;} Select ?p where { Q4 Who produced films starring Natalie Portman? ?f type Film; Natalie Portman ?f producer ?p;} Select ?f where { DBPedia In which films did Julia Roberts as well as Richard Gere ?f type Film; Q5 Richard Gere &QALD play? ?f starring ?p; ?p name “Roberts, Julia”} Select ?u where { List all episodes of the first season of the HBO television HBO, Q6 ?s name “The Sopranos”; series The Sopranos! first ?u series ?s;} Select ?f where { In which films directed by Garry Marshall was Julia ?f type Film; Q7 Julia Roberts Roberts starring? ?f director ?p; ?p name ”Marshall, Garry”;} Select ?u where { Which software has been developed by organizations ?c type Organisation; Q8 California founded in California? ?u developer ?c; ?u type Software;} Select ?s where { ?s type Place; gold, Q9 Which U.S. states possess gold minerals? ?s country ?g; mineral ?g name “the United States”;} Select ?u where { Q10 Which countries in the European Union adopted the Euro? ?u type Country; Euro ?u ethnicGroup European Union;}
Table 16: Sample QALD Queries over DBPedia