Efficient Incremental Validation of XML Documents

Transcription

1 Efficient Incremental Validation of XML Documents ICDE 2004, Boston Danilson Barbosa, Alberto O. Mendelzon, Leonid Libkin, Laurent Mignet, Marcelo Arenas University of Toronto Barbosa et.al: Efficient Incremental Validation of XML Documents p.1/20

2 Overview Problem Statement Static Validation Incremental Validation Evaluation Barbosa et.al: Efficient Incremental Validation of XML Documents p.2/20

3 Problem Statement Document Validity: A DTD D is a grammar that defines a set of documents L(D); each document in L(D) is said to be valid with respect to D. Validation Problem: Given a DTD D and an XML document X, is it the case that X L(D)? Incremental Validation Problem: Let U be some update operation; given X L(D), is it the case that U(X) L(D)? Update Operations: Delete or Insert a sub tree. Update = Delete + Insert Related Work: Suciu,... Barbosa et.al: Efficient Incremental Validation of XML Documents p.3/20

4 Document Type Definitions structural constraints: allowed nesting of elements attribute constraints: attribute values, IDs, IDREFs Example: <!ELEMENT a (b* (c, b*))> <!ATTLIST a w CDATA #IMPLIED x (1 2 3) #IMPLIED y ID #REQUIRED z IDREF #REQUIRED> Barbosa et.al: Efficient Incremental Validation of XML Documents p.4/20

5 Structural Validation structural constraints restricted to 1-ambiguous regular expressions parse with 1 token look-ahead mapping to unambiguous grammar is possible by subscripting equal symbols Construct Glushkov-automaton for expression E of length n with the following properties: construction in O(n 2 ) time 1 to 1 mapping of states in the automaton to positions in the regular expression, thus O(n) space Barbosa et.al: Efficient Incremental Validation of XML Documents p.5/20

6 Validation Attribute Constraints Types of attributes: validating CDATA or enumeration is trivial IDs need to be unique IDREF and IDREFS need to reference some existing ID ID, IDREF, and IDREFS require some work Participation Constraints: #REQUIRED or #IMPLIED trivial to validate Barbosa et.al: Efficient Incremental Validation of XML Documents p.6/20

7 Complexity of Validation: SAX vs. DOM SAX good for static validation during insertion or bulkload (avoid prior materialization) DOM for updates: assume log( D ) access time to nodes in D. assume SAX-like interface for insertions and DOM-like interface for updates and deletes. Barbosa et.al: Efficient Incremental Validation of XML Documents p.7/20

8 Complexity of Static Validation 1. SAX (depth-first-traversal): validate O(h) elements simultaneously one automaton per element keep a stack for the state of each automaton O( D log DT D ) time and space complexity. 2. DOM (validate each item at a time) O( D (log D + log DT D )) time and O(log D + log DT D ) space complexity. 3. Validation of attribute constraints for IDs O( D log D ) time and O( D ) space. Barbosa et.al: Efficient Incremental Validation of XML Documents p.8/20

9 Update Operations on Elements Append(p,y): insert y as child of p. InsertBefore(x,y): insert y as immediate left sibling of x. Delete(x): delete x from the document. (x is not the root of the document) Barbosa et.al: Efficient Incremental Validation of XML Documents p.9/20

10 Cost of Insertions Structural Validation: static validation of the subtree to insert O( D log DT D ). incremental validation of the resulting document. update the structure of the document O( D log D ). Attribute Constraints: only meaningful on the complete document. Barbosa et.al: Efficient Incremental Validation of XML Documents p.10/20

11 Cost of Deletions Structural Validation: incremental validation of the resulting document. update the structure of the document O( D log D ). Barbosa et.al: Efficient Incremental Validation of XML Documents p.11/20

12 Observation Update affects only the content of the element being updated revalidate only this element. should outperform static validation of the complete document Barbosa et.al: Efficient Incremental Validation of XML Documents p.12/20

13 Revalidation Approach store with each node state information of the automaton that validates this node requires O( D log DT D ) auxiliary storage. Barbosa et.al: Efficient Incremental Validation of XML Documents p.13/20

14 Appends or Deletions at the End Append(p,x): lookup the state information of p O(log D ) time check if the automaton still reaches an accepting state O(log DT D ) time Delete(x): lookup the state information of x O(log D ) time check if the automaton still reaches an accepting state with the left sibling as last element O(log DT D ) time Both: O(log D + log DT D ) time Barbosa et.al: Efficient Incremental Validation of XML Documents p.14/20

15 Example for Append regular expression a: (b 1 * (c, b 2 *)) append b automaton: s0 document fragment: a b c c s2 b s3 b s3 b? s1 b s2 b s3 b Barbosa et.al: Efficient Incremental Validation of XML Documents p.15/20

16 Arbitrary Deletions and Insertions Delete(x): lookup the state information of the left sibling of x O(log D ) time revalidate beginning with the left sibling of x and resuming with the right sibling of x optimizations are possible when states are repeatedly reached during revalidation InsertBefore(x,y): similar to Delete(x). both O( w (log D + log DT D )) time, w is the size of the content model for the node to revalidate. Note: w = O( D ) Barbosa et.al: Efficient Incremental Validation of XML Documents p.16/20

17 Example for Delete regular expression a: (b 1 * (c, b 2 *)) delete c automaton: s0 old fragment: a new fragment: a b c c s2 b s3 b s3 b s3 b s1 b s1 b s1 s1 b s2 b s3 b Barbosa et.al: Efficient Incremental Validation of XML Documents p.17/20

18 Improvents on Restricted DTDs For 1,2-conflict-free DTDs: limit revalidation to smaller fragments of the content model (as in the last example) incremental revalidation in O(log D + log DT D ) time and O( D log DT D ) auxiliary space For conflict-free DTDs: no repeated symbols in a regular expression, e.g a: ((a b), c*) incremental revalidation in O(log D + log DT D ) time and constant auxiliary space Barbosa et.al: Efficient Incremental Validation of XML Documents p.18/20

19 Experiments Barbosa et.al: Efficient Incremental Validation of XML Documents p.19/20

20 Summary complexity numbers depend on the representation of the documents and the automaton. only state information need to be materialized additionally. experiments show benefits of incremental validation Barbosa et.al: Efficient Incremental Validation of XML Documents p.20/20