Repair of XML documents
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1 Repair of XML documents (w.r.t. given T) Robert Surówka 1
2 Outline of the problem onvert given xml such that it will be valid w.r.t to given T? Should the conversion have some other features? Should it use minimum possible number of operations? What operations do we allow? How important this decision is? repair? Robert Surówka 2
3 Why this problem is important? Integrating XML databases Putting into existing XML database XML documents found in the Web crawling (to give structure to the data, to make it more usable easier to search through, combine, aggregate) Robert Surówka 3
4 Sample repairs Input document <!ELEMENT (((( ), )*) )> <!ELEMENT ()> <!ELEMENT (?)> Possible repairs Robert Surówka 4
5 Sample repairs Input document T F T F T F <!ELEMENT ((, (T F))*)> <!ELEMENT (#PT)> <!ELEMENT T (#PT)> <!ELEMENT F (#PT)> 3n times Even when considering only shorterst repair paths there is 2 n of repairs Robert Surówka 5
6 Operations - basics dd a leaf elete a leaf Rename a node E Robert Surówka 6
7 Operations - subtrees dd a minimal subtree E elete a subtree E Robert Surówka 7
8 Operations - nodes dd a node E elete a node E E Robert Surówka 8
9 Operations - shifts Shift a node E E Shift a subtree E F Robert Surówka 9 E F
10 Sample existing algorithms Ph dissertation May 2007 Operations used: - dd a subtree - elete a subtree - Rename a node Nobutaka Suzuki IPSJ igital ourier Vol. 2 ecember 2006 Operations used: - dd a node - elete a node - Rename a node pproximate omplexity: O( t ( S 2 R + S R lg( S R ))) pproximate omplexity: 2 w 4 t 2 r 2 ) t set of nodes of the given tree, S parameter bounded by size of the T, R - maximum number of siblings in given tree, - set of labels in the T, w maximum degree of a node in the given tree, r maximum length ofa regular expression in the T Robert Surówka 10
11 1. We have algorithms that find some shortest repair path of given XML document. 2. Operations that algorithm allows have a crucial impact on the repair. If 2 algorithms have sets of supported operations such that neither of them includes the other then neither of the algorithms always finds a shorter repair than the other. 3. omplexity of already known algorithms is sufficiently fast for most uses. 4. already have? Robert Surówka 11
12 Understanding an XML document <!ELEMENT epartment (ean?, Employees?)> <!ELEMENT Staff (Name*)> <!ELEMENT ean (Name?)> <!ELEMENT Faculty (Name*)> <!ELEMENT Employees (Faculty?, Staff?, Name*)> <!ELEMENT Name (#PT)> epartment epartment ean Employees Employees Foo There is a dean, whose Foo department been elected yet) Robert Surówka 12
13 n unwelcomed repair data corruption <!ELEMENT epartment (ean?, Employees?)> <!ELEMENT Staff (Name*)> <!ELEMENT ean (Name?)> <!ELEMENT Faculty (Name*)> <!ELEMENT Employees (Faculty?, Staff?, Name*)> <!ELEMENT Name (#PT)> Operations: 1. dd a node 2. elete a node 3. Rename a node epartment Employees Repair epartment Employees ean Foo Moreover it seems that no matter what operations algorithm would support, always a data corruption may happen 13
14 Idea 1. User imposes constraints on possible repairs (e.g. a constraint and any subtree rooted at ean prevent the erroneous repair from previous example). 2. Repair attempt is undertaken, and either valid (w.r.t. given constraints) repair is done or information than no such repair exists is returned. Realization 1. n appropriate constraint language needs to be defined. 2. repair algorithm must be developed that would be able to work with those constraints. Robert Surówka 14
15 lternative solution lot of work is done in solving a problem stated like this: 1, update script S changing it to T 2 and XML document X in 1 2 So one could just define some source and edit scripts transforming them to T in the database. Then transformation of given will be far more probable E.g. Nobutaka Suzuki: On Inferring K Optimum Transformations of XML ocument from Update Script to T. OM 2008: Robert Surówka 15
16 hoosing language reating a new language The language will be well tailored to needs (and therefore it may be more compact and convenient) More work would be needed to create that language as well as tools for it Use an existing language: Many of users will be already familiar with the language If for our needs some small tweaks to the language would be needed it may confuse the users The language can evolve Robert Surówka 16
17 onstraint language proposal Expression () (()) (,) (,*,) (+,,[1-2,5<],) Meaning Nodes have to be preserved If node has a child, then in output both of them have to be preserved in that configuration If node has a descendant, then in output both of them have to be preserved in that configuration (but may be e.g. promoted from grandchild to child) If node has children, in that order, and there are no other siblings between and then in output the three of them have to be preserved in that configuration If node has children, in that order then in output the three of them have to be preserved in that configuration If node has children, in that order, and has at least one left sibling and there are 1, 2 or more than 5 other siblings between and then in output that configuration has to be preserved (but, for example in input may have exactly one left sibling, but in output it may have 2 left siblings F,G). Robert Surówka 17
18 onstraint language proposition Special character or construction Meaning ~ Not exist (,*,~) $ $() - Has to be deleted (-,) Example l Level [l:<4,6]() s Sibling index ([s:<2,last]) ns Number of siblings ([s:3; ns:odd]) nc Number of children [nc:1-10,~5] nd Number of descendants [nd:<=3] nl Number of leaves among descendants [nl:even,3] t Target ([s:2; tc:<3]) id Identifier [id:1](([l:>2*l(1)])) Robert Surówka 18
19 Possible languages to use Twig Query Twig query (also knows as tree pattern query) It is a pair Q=(T,F) where T is node- labeled and edge- labeled tree with a distinguished x T and F is a boolean combination of constraints of nodes. Node labels are variables like $x or $y - - descendent) onstraints have form $x.tag = TagName or $x.data relop val, where $x.data denotes the data content of node $x, and relop is one of =, <,,,. In overall a Twig query (over an XML) is similar in concept to a selection condition in relational algebra Source: Laks V. S. Lakshmanan: XML Tree Pattern, XML Twig Query. Encyklopedia of atabase Systems 2009 : Robert Surówka 19
20 Possible languages to use Twig Query Twig queries could in our project can be used to specify subtrees that cannot be changed by repairing algorithm Twig query finds set of subtrees of a tree that conform to condition of the query Source: Laks V. S. Lakshmanan: XML Tree Pattern, XML Twig Query. Encyklopedia of atabase Systems 2009 : Robert Surówka 20
21 Possible languages to use - XPath Xpath There are many versions of Xpath: Regular Xpath First- Order Xpath ggregate Xpath ggregate XPath with position arithmetic (Good source article about Xpath: ) Robert Surówka 21
22 Possible languages to use - Regular XPath Regular Xpath query grammar: Q t is the binary reachability relation on the nodes of tree t defined by the query Q Robert Surówka 22
23 Possible languages to use - Regular XPath Preservation constraints: Robert Surówka 23
24 Possible languages to use - Regular XPath Purity constraints: Robert Surówka 24
25 Possible languages to use - Regular XPath Problem of constraint satisfability: is Exptime- hard. It means that in order to find practically usable algorithm it needs to be Probabilistic pproximate Or both Robert Surówka 25
26 Future work Eventually defining the constraints language Getting an idea which constraints types are most usable for potential users (some survey?) Proposing a polynomial- time algorithm to solve the problem (or at least one being able for any problem instance to find an approximate solution with some probability) Robert Surówka 26
27 Questions? Robert Surówka 27
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