What is Cyclic Graph

Composite objects represented as directed graphs are an important data structure that require efficient support Web and document databases (Abiteboul, Cluet, Christophides, Milo, Moerkotte, & Simon, 1997; Chen & Aberer, 1998, 1999; Mendelzon, Mihaila, & Milo, 1997; Zhang, Naughton, Dewitt, Luo, & Lohman, 2001), CAD/ CAM, CASE, office systems, and software management. It is cumbersome to handle such objects in relational database systems when they involve ancestor-descendant relations (or say, reachability relations). In this article, we present a new graph encoding based on a tree labeling method and the concept of branchings that are used in the graph theory for finding the shortest connection networks. A branching is a subgraph of a given digraph that is in fact a forest, but covers all the nodes of the graph. Concretely, for a DAG G (directed acyclic graph) of n nodes, the space needed for storing its transitive closure can be reduced to O(b·n), where b is the number of the leaf nodes of G’s branching. Such a compression is, however, at the expense of querying time. Theoretically, it takes O(logb) time to check whether a node is reachable from another. The method can also be extended to digraphs containing cycles.