Efficient Incremental Validation of XML Documents

1. Efficient Incremental Validation of XML Documents Denilson Barbosa Alberto O.Mendelson Leonid Libkin Laurent Mignet Marcelo Arenas Presented by Daria Barger Daria Barger – DB Seminar

2. Outline • Introduction • Types of constraints • Update operations • Incremental validation • Experiments • Conclusions • Future work Daria Barger – DB Seminar

3. Introduction • The problems of storing and querying XML documents have attracted a great deal of interest. • Other aspects of XML data management, however, have not yet been satisfactorily explored. • Among them is the problem of checking that documents are valid with respect to their specifications, and that they remain valid after updates. Daria Barger – DB Seminar

4. DTD • One popular form of XML document specification is the Document Type Definition (DTD). • 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 . Daria Barger – DB Seminar

5. The Validation Problem The validationproblem is: Given a DTD D and an XML document X, is it the case that X  L(D) ? The incrementalvalidationproblem is: Let U be some update operation. Given X  L(D), is it the case that U(X)  L(D)? Daria Barger – DB Seminar

6. Validation of structural constraints Content Model: Element- valid iff the string formed by concatenating its children elements belongs to L(E), the language denoted by E. Elements are declared in DTD by rules of the form: <!ELEMENT e c> <?xml version="1.0"?> <!ELEMENT db (person*)> <!ELEMENT person(name, dep, email, tel*)> <!ELEMENT name (#PCDATA)> <!ELEMENT dep(#PCDATA)> <!ELEMENT email(#PCDATA)> <!ELEMENT tel(#PCDATA)> Content Model: #PCDATA – validation can be done trivially Daria Barger – DB Seminar

7. Validation of attributes Attributes validation is trivial, except for ID and IDREF attribute types. Valid XML document should hold: • Values of all ID attributes are unique • Value of each IDREF attribute must be equal to the value of some ID attribute Daria Barger – DB Seminar

8. 1-unambiguous regular expressions Marking: The specification of XML DTDs restricts the regular expression used for defining element content to be 1- unambiguous (deterministic). Position – subscripted symbol in E`. For given position x, Χ (x) denotes a corresponding (unmarked) symbol in Σ. For example: pos(E’) = {a,b1,b2,c} Χ (b1) =b Daria Barger – DB Seminar

9. 1-unambiguous regular expressions A regular expression E is 1- unambiguous if and only if for all words u,v,w over the subscripted alphabet pos(E) and all x,y in pos(E), the conditions uxv, uyw  L(E`) and x≠y imply Χ(x) ≠ Χ(y) Which regular expression is deterministic? • (ab)|(ac) • a(b|c) • a(a+b)*ac Daria Barger – DB Seminar

10. The Glushkov automaton for Regular Expressions set of positions that appear as the first symbol of some word in L(E’) set of positions that appear immediately after position x in some word in L(E’) set of positions that appear as the last symbol of some word in L(E’) Daria Barger – DB Seminar

11. Update operations A p A A y A A A A A A A A A A A A • Append(p,y) - insert element y as the last child of element p. Append Daria Barger – DB Seminar

12. Update operations (2) A A A A A • InsertBefore(x,y) – insert element y as immediate left sibling of element x.(This operation is not defined if x is the root of the document). A A A x A A A y A A Insert Before A A Daria Barger – DB Seminar

13. Update operations(3) A A A A A A A A A A A A A A A x • Delete(x) – delete element x from the document. Note that if x is the root of the document the operation is trivially valid. Delete(x) Daria Barger – DB Seminar

14. Observation The incremental validation concerns only the content of the element where the update takes place. For example, after an Append(p,y) operation only the content of p needs to be revalidated. Daria Barger – DB Seminar

15. The approach wk w2 w1 p w3 … • Together with the i-th child of p we store the value of for the automaton that validates the content model of p. • This requires auxiliary storage of size O(n log d), where n is a size of XML document, d is size of DTD Daria Barger – DB Seminar

16. Append at the end wk w2 w1 p y w3 … Append(p,y) operation Daria Barger – DB Seminar

17. Arbitrary insertions and deletions wk w2 w1 wi Delete(x) operation p … … Problem: Complexity Daria Barger – DB Seminar

18. 1,2 Conflict Free Regular Expression Possible solution: Let’s consider E=a(b1*|cb2*) W=acb…b. All b’s match state b2 Delete c from w, receive w’=ab…b Now all b’s match state b1 We should re - validate the entire string This condition does not hold always, e.g. Daria Barger – DB Seminar

19. Definition of 1,2 Conflict-free Let E be regular expression over alphabet Σ Follow(E,x) – set of position in E that can follow x in some path through E. Define such that E is 1,2 conflict - free regular expression if: Daria Barger – DB Seminar

20. Restricted forms of DTD • 1,2 Conflict Free DTD • There is no “flipping” between automata states after the update. • The per update complexity for 1,2 Conflict Free DTD is O(log n + log d) time and O(n log d) auxiliary space. • Conflict-free DTD: • No repeated symbols. • The per update complexity: O(log n + log d) and constant auxiliary space. Daria Barger – DB Seminar

21. Incremental validation of ID and IDREF for adding element Append(p,y) and InsertBefore(x,y) operations require checking that no two ID attributes are the same and every IDREF attribute in y refers to some existing document values. The complexity: O(|y|log n) time and linear auxiliary space. |y| = size of added subtree. Daria Barger – DB Seminar

22. Incremental validation of ID and IDREF for deleting element After Delete(x) operation we have to check that there is no subtree rooted at x that contains a node that has an ID attribute referenced by some other node that is not a descendant of x. c b a Checking reference counter in delete requires O(log n) time. Updating reference counter in insert/removing IDREF attribute: O(h log n) time. Daria Barger – DB Seminar

23. Valid Insertion 1e+08 Incr CF – Incr 1.2 CF – Incr Arb – Full Arb – Full CF - 1e+06 Time [micro sec] 10000 100 64K 512K 4M 32M 256M 2G Document size Daria Barger – DB Seminar

24. Valid Deletion 1e+08 Incr CF – Incr 1.2 CF – Incr Arb – Full Arb – Full CF - 1e+06 Time [micro sec] 10000 100 64K 512K 4M 32M 256M 2G Document size Daria Barger – DB Seminar

25. Invalid Deletion Incr CF – Incr 1.2 CF – Incr Arb – Full Arb – Full CF - 1000 Time [micro sec] 100 10 64K 512K 4M 32M 256M 2G Document size Daria Barger – DB Seminar

26. Conclusions • Handled insertion and deletion of subtrees (not leaf nodes only). • Validated ID and IDREF attributes. • Characterize a class of DTDs appearing to capture most real life DTDs that admits a log time and constant space incremental validation algorithm. • Conducted experiments showing that the method is practical for large data documents and behaves much better than full revalidation. Daria Barger – DB Seminar

27. Future Work Handling complex updates, involving several insertions and deletions as a single transactions. Daria Barger – DB Seminar