Modeling Visibility in Hierarchical Systems

We consider hierarchical systems where nodes represent entities and edges represent binary relationships among them. An example is a hierarchical composition of Web services where the nodes denote services and edges represent the parent-child relationship of a service invoking another service. A fundamental issue to address in such systems is, for two nodes X and Y in the hierarchy whether X can see Y, that is, whether X has visibility over Y. In a general setting, X seeing Y may depend on (i) X wishing to see Y, (ii) Y wishing to be seen by X, and (iii) other nodes not objecting to X seeing Y. The visibility could be with respect to certain attributes like operational details, execution logs, security related issues, etc. In this paper, we develop a generic conceptual model to express visibility. We study two complementary notions:

sphere of visibility

of a node X that includes all the nodes in the hierarchy that X sees; and

sphere of noticeability

of X that includes all the nodes that see X. We also identify the dual properties, coherence and correlation, that relate the visibility and noticeability notions. We propose elegant methods of constructing the spheres with these properties.