Structural Controllability for a Class of Complex Networks With Root Strongly Connected Components

Strongly connected components-Algorithm for finding the strongly connected components of a graph

A directed graph G (V, E) is strongly connected if and only if, for any pair of vertices X and Y from V, there exists a path from X to Y and a path from Y to X. In Computer Science, the partition of a graph in strongly connected components is represented by the partition of all vertices from the graph, so that for any two vertices, X and Y, from the same partition, there exists a path from X to...

Twinless Strongly Connected Components

Tarjan [9], describes how depth first search can be used to identify Strongly Connected Components (SCC) of a directed graph in linear time. It is standard to study Tarjan’s SCC algorithm in most senior undergraduate or introductory graduate computer science algorithms courses. In this paper we introduce the concept of a twinless strongly connected component (TSCC) of a directed graph. Loosely ...

Parallel Algorithms for Detecting Strongly Connected Components

Controllability for a Class of Parallelly Connected Polynomial Systems

Null controllability for a class of parallelly connected discrete-time polynomial systems is considered. We prove for this class of systems that a necessary and sufficient condition for null controllability of the parallel connection is that all its subsystems are null controllable. Consequently, the controllability test splits into a number of easy-to-check tests for the subsystems. The test f...

Decremental maintenance of strongly connected components

We consider the problem of maintaining the strongly connected components (SCCs) of an n-nodes and medges directed graph that undergoes a sequence of edge deletions. Recently, in SODA 2011, Łącki presented a deterministic algorithm that preprocess the graph in O(mn) time and creates a data structure that maintains the SCCs of a graph under edge deletions with a total update time of O(mn). The da...