For a geometric constraint system based on directed graph,matching direction and distribution of constraints and scale of strongly-connected sub-graphs in the directed graph affect the efficiency of constraint solving directly.

Due to the actual needs like the references and , the Algorithm for strongly-connected component of graph based on DFS technology is expanded and improved in order to make it more complete.

Finally, the analysis approaches of fault propagation based on strongly-connected components (SCCs) are presented, which provide the theoretical foundations for the applications based on the SDG approach in the area of fault diagnosis and so on.

We discovered the existence of a single large weakly-connected and a single large biconnected component, and confirmed the expected lack of a large strongly-connected component.

We consider several problems relating to strongly-connected directed networks of identical finite-state processors that work synchronously in discrete time steps.

In this paper the structure of large-scale systems is firstly discussed. It is pointed out that each such system cah be decomposed into a multi-level structure, each level of which is composed of "minimal strongly connected subsystems" and only the highest level is a "Simply connected subsystem". Then concepts "stability strength" and "Connectivity strength" are introduced. Such allows the stability conditions of the large-scale system to have simple forms of the same type, having appavent physical interpretations....

In this paper the structure of large-scale systems is firstly discussed. It is pointed out that each such system cah be decomposed into a multi-level structure, each level of which is composed of "minimal strongly connected subsystems" and only the highest level is a "Simply connected subsystem". Then concepts "stability strength" and "Connectivity strength" are introduced. Such allows the stability conditions of the large-scale system to have simple forms of the same type, having appavent physical interpretations. In the last section the stabilization problem is considered. Multilevel structure and concepts of stability strength and connectivity strength much faciliate the selection of local feedbach controllers which are minimally necessary.

A new algorithm of performing the transitive closure of a directed graph is presented. Each of the strongly connected components in the graph is 'compressed' to a single node in the first place. The graph is trimmed into a spanning tree without any cycle. At the same time, all reflexive edges and forward edges are eliminated in the process. The union operation of non-disjoint sets is used to compute transitive relations of a graph. The algorithm is faster, in case e<

For the decentralized control system, though quite a few works about the stuctural characteristic of the system having fixed modes and the necessary and sufficient conditions of D controllability had been done in recent years, the relationship between fixed mode and D-controll-ability is nowadays being less considered. As viewed from D-controllability, the non-existence condition of fixed mode is discussed in this article in order to clarify further the interrelation between fixed mode and D-controllability....

For the decentralized control system, though quite a few works about the stuctural characteristic of the system having fixed modes and the necessary and sufficient conditions of D controllability had been done in recent years, the relationship between fixed mode and D-controll-ability is nowadays being less considered. As viewed from D-controllability, the non-existence condition of fixed mode is discussed in this article in order to clarify further the interrelation between fixed mode and D-controllability. Thus a basis can be laid down for systematically studying the stability and pole assignment problems.Summary. In accordance with D-controllability, existence conditions of a given system having no fixed mode are discussed, a sufficient condition and a necessary and sufficient condition are derived therefrom as follows.Theorem 1. Let ∑ be a system described asand ∑ be jointly observable and be possessed of D-controllability for eachwith output feedback,no fixed mode will exist in.WhereX is the n-dimensional state vector of ∑, u the i th m; dimensional input vector, yj the j-th pi-dimensional output vector, and A,Bi and Cj the real matrices having appropriate dimensions.Theorem 2. Let system ∑ described as above be jointly controllable and observable and strongly connected, then no fixed mode will exist in if and only if the given system is possessed of D-controllability for each ui, i∈{1,2,......,N}.