1. Query Caching and View Selection for XML Databases Bhushan Mandhani Dan Suciu University of Washington Seattle, USA

2. Caching in Query Processing Buffer Cache: In-memory pool of disk pages. Semantic Cache:  Stores query results instead.  Can be in-memory or on disk.  Proposed in [Franklin et al., VLDB 96] for use in client- server systems.

3. Semantic XPath Cache A cached query result is a materialized view. View V answers query Q if there exists C s.t C º V = Q C, V & Q are all XPath here. Cache contains some views {V 1,…,V n }. Query Q is a hit if some V i answers it.

4. Motivation for the Semantic Cache C º V = Q : a cache hit results in a simpler query, on a much smaller XML fragment. Cache hits were processed two orders of magnitude faster than misses. Can also be maintained outside the database  Ex: application tier. Application tier caching for database-driven websites has become increasingly popular [Mohan et al., SIGMOD 02].

5. Example Illustrating C º V = Q V = /a[u[@v]/w]/b[x//y] Q = /a[u[w]/@v]/b[x/y//z]/c C = /b[x/y//z]/c

6. The Query/View Answerability Problem Given view V and query Q, does V answer Q, and if yes, then what should C be?

7. XPath Tree Patterns XPath queries have natural representation as tree patterns. E.g. If Q = a[v]/b[@w=''val1''][x[.//y]]//c[z>val2] The Query Axis is the path from the root node to the result node. The Query Depth is the number of axis nodes. Prefix(Q, k) is the query obtained by truncating Q at its k-th axis node.  E.g. Prefix(Q, 2) = a[v]/b Preds(Q, k) is the set of predicates of the k-th axis node of Q.  E.g. Preds(Q, 2) ={[@w=''val1''], [x[.//y]]}

8. XPath Containment A С B if the result of A will always be a subset of the result of B. Checking XPath containment is coNP-complete [Miklau & Suciu, PODS 02]. A containment mapping maps nodes in B’s tree pattern to those in A’s, and establishes A С B.  It is a sound but incomplete condition.  It can be determined in polynomial time. Containment is different from answerability.  E.g. let A = /a[x]/b, B = /a/b

9. Criteria for Query/View Answerability “Rewriting XPath Queries using Materialized Views”, Xu and Ozsoyoglu, VLDB 2005

10. An Example of Answerability Checking  Let V = /a[u[@v]/w]/b[x//y]  Let Q = /a[u[w]/@v]/b[x/y//z]/c  Prefix(V, 2) = /a[u[@v]/w]/b and Prefix(Q, 2) = /a[u[w]/@v]/b. The first condition is satisfied.  Preds(V, 2) = {[x//y]} and Preds(Q, 2) = {[x/y//z]}. The second condition is also satisfied.

11. Two Theoretical Results Theorem: If two tree patterns are minimal, and containment mappings exist both ways, then they are isomorphic. Theorem: If some view V answers query Q, then C can be set to the subtree of Q rooted at its k-th axis node, where k is the query depth of V.

12. The Cost of Answerability Checking Answerability checking involves tree operations:  Checking isomorphism between trees.  Looking for containment mappings between trees. Cache lookup by checking each view could give a high lookup overhead. Our Solution: Check answerability by string matching. This will be:  Cheaper  Amenable to indexing in a standard RDBMS.

13. Checking Tree Isomorphism We represent each tree pattern with its “normalized” query string. To obtain the normalized query:  At each axis node, do a DFS into each predicate subtree.  Before returning from a node, append its children node labels to its label, in lexicographic order.  Concatenate all axis node labels to get the normalized query.

14. Checking Predicate Containment For the tree of each predicate in Preds(Q, k), generate all trees that “containment map” to it. ConPreds(Q, k) is the set of normalized predicates obtained from these generated trees.

15. String-Based Criteria for Answerability The second condition is tweaked to correctly support comparison predicates.

16. Cache Organization Let V = /a[u]/b[v][@x=50][y/z=“str”]. Insert into XmlData (‘ ’). Record viewId. Insert into Prefix (‘/a[u]/b’). Record prefixId. Insert into View (viewId, prefixId, ‘@x=50’, ’y/z=“str”|v’).

17. Cache Lookup Prefix(V, k) = P.prefix = Prefix(Q, k). V.pred Є Preds(V, k) and V.pred Є ConPreds(Q, k).

18. Cache Warm-up as View Selection Given the warm-up workload W, we generate another workload S. S is likely to have overlap with the test workload. Problem: Choose some m views from S which together answer a maximal subset of S. This is a variant of the set cover problem, which is NP-complete. We use a variant of the greedy approximation algorithm for set cover.

19. Experimental Setup The data instance was a 300 MB XML document created using the XMark generator. Expts run on a Pentium 4, 512 MB RAM machine. SQL Server 2005 beta used for storing the XML data as well as the cache. We compare our cache with a naïve cache which stores (query string, result XML) pairs.

20. Query Workloads Used We implemented our own XPath query generator for creating workloads for our expts. Query structure is generated randomly. Value for each predicate is obtained by sampling from its set of values taken, using Zipf distribution. Queries with depths 3, 4 and 5 were given 2, 2 and 3 predicates respectively.

25. Conclusions We defined a notion of query/view answerability for XPath. We showed how an efficient semantic cache based on these ideas can be employed. We demonstrated the scalability of cache lookup, and performance gains in query processing.