A TREE BASED ALGEBRA FRAMEWORK FOR XML DATA SYSTEMS Ali El bekai, Nick Rossiter School of Informatics, Northumbria University Email: ali.elbekai@unn.ac.uk , nick.rossiter@unn.ac.uk

Overview Framework in algebra for processing XML data. Review related work Develop a simple algebra, called TA (Tree Algebra), for processing storing and manipulating XML data as trees Describe input and output of the algebraic operators Define the syntax of relationships/operators and their semantics in terms of algorithms. Examples are given in the domain specific XML query language. Discuss closure and application

Related Work IBM (Beech & Rys, 1999) Lore (McHugh et al 1997) YATL (Christophides et al 2000) Niagara (Galanis et al 2001) AT&T (W3C) TAX (Jagadish et al 2001) Problems identified in complexity and generality

Tree Algebra True tree Leaves of tree Two types of operators Each node one parent but many children Root node Leaves of tree Correspond to different sources – object relational Two types of operators Algebraic operators Relational operators

Concepts in Tree Model Root (ultimate ancestor or parent) Node (parent or child) Edge (link from a parent to a child) Leaf (atomic values, nodes with no children) Path (sequence of edges between nodes) Descendants (all successor nodes for a node) Ancestors (all parent nodes for a node)

Mappings XML Document  Tree Element  Node (root, parent, child) Leaf  child node, atomic values Attribute  function, values

Example XML Tree Root – collection element; object1, object3 – sub-elements;

Algebraic Relationships Comparison of two trees Universal (unary) Defines tree containing all information Similarity (binary) Two trees have the same structure Equivalence (binary) Two trees are indistinguishable Subsumption (binary) One tree is subsumed in another

Example Equivalence Relationship XML Tree Collection3 is equivalent to Collection4: Same node structure, no mismatch in content

Example Subsumption Relationship Collection3 is part of collection4 (structure and content)

Algebraic Operators for Trees Join (binary, input two trees, output one tree, commutative, associative) Joined on a predicate Union (binary, input two trees, output one tree, commutative, associative, disjoint) Summing trees together Complement (binary, input two trees, output one tree, not commutative, not associative) Nodes in one tree not found in another

Algorithm for Complement Operator // Input two XML document or two DOC tree (DOCn Tree, DOCm Tree) // Output DOCnm Tree = (DOCn Tree - DOCm Tree) 1 Start from root node DOCn If root node DOCn Tree and root node DOCm Tree has parent/child node .1 Perform depth-first algorithm .2 If DOCn Tree has parent node not existing in DOCm Tree 2.2.1 set parent node DOCn Tree to the new DOCnm Tree 2.2.2 while parent node DOCn Tree has child node not existing in DOCm Tree 2.2.2.1 set child node DOCn Tree to DOCnm Tree 2.2.2.2 if child node DOCn Tree has leaf node not existing in DOCm Tree 2.2.2.2.1 set leaf node DOCn Tree to DOCnm Tree 2.2.2.3 set null to DOCnm Tree 2.2.3 repeat 2.3 set null to DOCnm Tree 3 Set root node to DOCnm Tree and terminate end/terminate

Projection Algebra Operator (unary, input one tree, output one tree): Example Eliminates nodes other than those specified Projection of object3

Algebra Operators (continued) Select (unary, input one tree, output one tree) Filters nodes according to a predicate Expose (unary, input one tree, output one tree) Retrieve specific elements/nodes given by parent/child boundaries Vertex (unary, input one tree, output one tree) Creates the vertex encompassing all nodes created by the expose operator

Algorithm for Complement Operator // Input one DOC tree or one XML document // Output one DOC tree or one XML document 1 start with entry point, it is the root node perform depth-first algorithm 2.1 if parameter is equal to the specific node needed to expose .1.1 return the specific node .1.2 set specific node in the new tree 2.2 if exposed element does not exist then terminate 3 end/terminate

Results Developed Domain specific algebra Tree algebra Algebraic relationships Universal, similarity, equivalence, subsumption Algebraic operators Join, union, complement, project, select, expose, vertex Closure – output is always a tree

Verification All operators: Case study: Presented as algorithms Implemented in java Case study: Virtual museum application Implemented code employed for satisfaction of museum requirements

Further Work Investigate Further experimentation Extent to which limitations in operators affects usability Does domain need extending? Further experimentation Examine feedback from museum study Look at further areas