1. GRIN – A Graph Based RDF Index Octavian Udrea Andrea Pugliese V. S. Subrahmanian Presented by Tulika Thakur

2. - Indexing mechanism for Graph based Queries. -GRIN : a tree data structure. -Large RDF datasets used : TAP, ChefMoz -Comparison with DB systems: Jena, Sesame, RDFBroker - Measure parameters - 1) Size of Index 2) Time taken to answer graph queries 3) Time taken to build the index

3. RDF graph queries The GRIN Index structure Query Answering Experimental evaluation

4. RDF Graph Example (extracted from ChefMox dataset)

5. RDF Graph Representation : An RDF triple has the form (s, p, v) where s ∈ U, p ∈ Up, v ∈ R. U denote a set whose elements are called URI References. L denote a set whose elements are called literals. Up ⊆ U denotes the set of properties. R = U ∪ L denotes the set of resources

6. Introduction to P-path Given an RDF graph D and a set P ⊆ Up, a P-path in D is a set {e1,..., eq}, with ej = (sj, pj, vj), such that ∀ j ∈ [1, q] ej ∈ D; ∀ j ∈ [1, q − 1] vj = sj+1; ∀ j ∈ [1, q] pj ∈ P. Intuitively, a P-path is a path in the RDF graph whose edge labels are all drawn from the set P. For Example Let P = {location, locatedIn}. The triples (ColdStone, location, Lincoln) and (Lincoln, locatedIn,NE/USA) constitute a P-path of length two in the graph.

7. Introduction to P-path P = {location,locat edIn} d(ColdStone,NE/USA) = 2 Triples = (ColdStone, location, Lincoln) and (Lincoln, locatedIn,NE/U SA)

8. RDF Graph Query An RDF graphical query is a 4-tuple (N, V, E, λn) where: N is a set of vertices; V is a set of variables; E = Es ∪ Ed is a set of edges, where E s ⊆ N × N × (V ∪ Up) and E d ⊆ N × N × 2^U p × IN. We call E s the set of single edges and Ed the set of double edges. λn : N →R ∪ V is a vertex labeling function.

9. RDF Graph Query The query can be expressed in SPARQL as: SELECT ?v1 ?v2 ?v3 WHERE {{(?v1 attire ?v3). (?v1 cuisine Italian)} {(?v2 attire ?v3). (?v2 cuisine Italian). (?v2 location Norfolk)} {(Norfolk locatedIn NE/USA)}} P-path

10. RDF graph queries The GRIN Index structure Query Answering Experimental evaluation

11. GRIN Index -Resources “closer” in the RDF graph are more likely to be part of the same answer Hence they should appear on the same page. -GRIN will group resources in circles around selected center resources -Query evaluation: Find the smallest circle that contains the answer -Evaluate query only on resources in that circle

12. Building a GRIN Index A GRIN index is a balanced binary tree such that: Each leaf node contains a set N l ⊆ Rof nodes s.t. for all leaf nodes l != l', N l ∩ N l' = ∅ ; Each non-leaf node t contains a pair (c, r), with c ∈ R and r ∈ IN. This is a very succinct representation of the set of resources in the graph at distance at most r of the resource c. We write this set as Nt = {c' ∈ R|d(c, c') ≤ r}. For any nodes x, y in the tree such that x is a parent of y, Nx ⊇ Ny.

13. Building a GRIN Index M = maximum number of RDF graph vertices per page. C = number of leaf nodes. |R|/C <= M d c = inter cluster distance function (i) Single link defines d c (S, S') = Min (d c (x, y)) where x ∈ S,y ∈ S' (ii) Complete link defines d c (S, S') = Max (d c (x, y)) where x ∈ S,y ∈ S' (iii) Average link defines d c (S, S') = (Σ(d c (x,y)))/ ( |S|×|S'| ) Where x ∈ S,y ∈ S'

14. Building a GRIN Index Cluster the vertices in C disjoint Sets using PAM Clustering algorithm. Repeat untill equilibrium is reached? For each intermediate leve, GRINBuld chooses a random node u, Computes its closest node v, and assignes a parent node (c,r) where c is selected from Nu U Nv

15. Building a GRIN Index

16. Building the index: the tree 16

17. Building the index: the tree 17

18. Building the index: the tree 18

19. RDF graph queries The GRIN Index structure Query Answering Experimental evaluation

20. Query Answering Derive Contraints from the query. Evaluate constraints against the nodes of GRIN Index d(?v1,NE/USA) ≤ 2, d(?v2, NE/USA) ≤ 2, d(?v2, Norfolk) ≤ 1), d(?v1, Norfolk) ≤ 3, d(?v1, Italian) ≤ 1, d(?v2, Italian) ≤1, d(?v3, NE/USA) ≤ 3, d(?v3, Norfolk) ≤ 2, d(?v3, Italian) ≤ 2.

21. Query Answering For any given node, REJECT or ACCEPT it. 1: Reject circle(c,r) if any constant in query is outside the circle 2: Reject circle(c,r) if we cannot guarantee that every variable in inside the circle. Is ?v1 in circle (Grivanti, 2)? d(Grivanti,?v1) ≤ d(Grivanti,Italian)+d(?v1,Italian) ≤ 2 So ?v1 can be satisfied.

22. RDF graph queries The GRIN Index structure Query Answering Experimental evaluation

23. RDF System : GRIN Does not store the data in the index, but points to it. The data is stored in a hash table. Only one computationaly iintensive operation – Clustering the leaf nodes. For 300MB data, indexi stored in 75MB and 320 MB is used for the hash table.

24. RDF System : Jena Stores RDF as (subject, property, value) in a relational table. Indexes on each of the three attributes. Translates SPARQL/RDQL into SQL. Too many self joins. Used 403MB for indexing on 300MB data.

25. RDF System : Sesame Supports RDF Schema inference Separates RDFS from the triple table Supports database schema generation based on the underlying RDF schema of a dataset The problem of too many joins still remain. Used 825MB for indexing on 300MB data.

26. RDF System : RDF Broker The database schema is built based on signatures – the set of properties used on a resource. Reduces the number of joins between tables. Used 950MB for indexing on 300MB data.

30. Discussiom Vertices in GRIN = resources in underlying RDF. Resources can be atmost |R|. Therefore, number of leaf nodes = O|R| GRIN s a binary tree, so height of tree = O(log 2 |R|) Worst Case complexity for index building = O(|R|^ 4* log 2 (|R|) ) Good for small sized data only.

31. Discussion Time complexity for Query Answering : Best Case - O(N) Worst Case - O(N!) Where N is the total number of vertices in the graphs to be matched, “Our experimental results show that GRINAnswer is often faster than Jena, Sesame and RDFBroker for certain types of graph-based queries.”

32. Discussion The query can be expressed in SPARQL as: SELECT ?v1 ?v2 ?v3 WHERE {{(?v1 attire ?v3). (?v1 cuisine Italian)} {(?v2 attire ?v3). (?v2 cuisine Italian). (?v2 location Norfolk)} {(Norfolk locatedIn NE/USA)}} No Way to represent P-path in SPARQL !! P-path

33. ThankYou!