Efficient evaluation of reachability query for directed acyclic XML graph based on a prime number labelling schema

Many schema labelling approaches have been designed to facilitate querying of XML documents. The proposed algorithms are based on the fact that ancestor–descendant relationships among nodes can be quickly determined. Schema labelling is a family of technologies widely used in indexing tree, graph, or structured XML graph, in which a unique identifier is assigned to each node in the tree/graph. The generated identifier is then used in indexing as a reference to the actual node so that structural relationship among the nodes can be quickly captured. In this paper, we extend the prime number schema labelling algorithm for labelling DAG XML graph. Our main contribution is scaling down the original XML graph size substantially based on the Strongly Connected Component (SCC) principles. Labelling each node in DAG with an integer that is the arithmetical multiplication of the prime number associating with the node and its parent label. The schema does not depend on spanning tree. Thus, subsumption hierarchies represented in a DAG can be efficiently explored by checking the divisibility among the labels. Also, it inherits dynamic update ability and compact size features from its predecessors. Our theoretical analysis and the experimental results showed that the generated labelled schema is an efficient and a scalable one for processing reachability queries on large XML graphs