Modeling and Exploring the Algebraic Properties of Hierarchical Structures
by Alexandra Meliou
Abstract:
The XML Language is becoming the new standard for storing and exchanging knowledge through the internet. XML data incorporate structure and data in one entity. The data model of XML is a graph representation of a collection of atomic and complex objects. Under certain conditions, the XML data model becomes a schema tree. Schema trees are rooted ordered labeled trees that express the structural relationships between the nodes of an XML document. Schema trees are used to represent not only XML documents, but also complex data. The main purpose of this thesis is to explore the algebraic properties of hierarchical structures. Given two or more trees we define new trees by applying operators like union, intersection, difference. These operators are defined in such a way that they obey laws similar to the ones of set theory. We study the conditions under which these operators are applicable, and we present algorithms to implement the operators and check their validity.
Citation:
Alexandra Meliou, Modeling and Exploring the Algebraic Properties of Hierarchical Structures, Athens, Greece, 2003.
Bibtex:
```@misc{Meliou-diploma,
Abstract = {The XML Language is becoming the new standard for storing and
exchanging knowledge through the internet. XML data incorporate structure
and data in one entity. The data model of XML is a graph representation of
a collection of atomic and complex objects. Under certain conditions, the
XML data model becomes a schema tree. Schema trees are rooted ordered
labeled trees that express the structural relationships between the nodes
of an XML document. Schema trees are used to represent not only XML
documents, but also complex data. The main purpose of this thesis is to
explore the algebraic properties of hierarchical structures. Given two or
more trees we define new trees by applying operators like union,
intersection, difference. These operators are defined in such a way that
they obey laws similar to the ones of set theory. We study the conditions
under which these operators are applicable, and we present algorithms to
implement the operators and check their validity.},
Author = {Meliou, Alexandra},
Howpublished = {Diploma thesis, National Technical University of Athens},
Title = {\href{http://www.dblab.ece.ntua.gr/pubs/uploads/DIPL-2003-07.pdf}{Modeling and Exploring the Algebraic Properties of Hierarchical Structures}},
Venue = {BSc},
address = {Athens, Greece},
month = {May},
Year = {2003}
}```