We address the problem of discovering routes in strongly connected planar geometric networks with directed links. We consider two types of directed planar geometric networks: Eulerian (in which every vertex has the same number of ingoing and outgoing edges) and outerplanar (in which a single face contains all the vertices of the network). Motivated by the necessity for establishing communicatio...

Structure-based approaches to diagnosis provide useful computational guarantees based on a device structure. In particular, these approaches can identify device structures for which the complexity of model-based diagnosis is guaranteed to be linear. Structure-based approaches, however, can fail to answer even the simplest diagnostic queries if the device structure is not well behaved (strongly ...

We propose an O(min{m+n logn,m log∗n}) to find a minmax strongly connected spanning subgraph of a digraph with n nodes and m arcs. A generalization of this problem called the minmax strongly connected subgraph problem with node penalties is also considered. An O(m logn) algorithm is proposed to solve this general problem. We also discuss ways to improve the average complexity of this algorithm.

We consider the DIRECTED STEINER NETWORK problem, also called the POINT-TO-POINT CONNECTION problem, where given a directed graph G and p pairs {(s1, t1), . . . ,(sp, tp)} of nodes in the graph, one has to find the smallest subgraph H of G that contains paths from si to ti for all i. The problem is NP-hard for general p, since the DIRECTED STEINER TREE problem is a special case. Until now, the ...

We consider how to maintain the topological order of a directed acyclic graph (DAG) in the presence of edge insertions and deletions. We present a new algorithm and obtain a marginally improved complexity result over the previously known O(||δ||log||δ||). In addition, we provide an empirical comparison against three existing solutions using random DAG’s. The results show our algorithm to out pe...

Several algorithms exist for decomposing strongly connected components (SCCs). To accommodate recent non-reversible trends in hardware, we focus on utilizing multi-core architectures. Specifically, we consider parallelizing SCC algorithms in the setting of an on-the-fly implementation (to be able to detect SCCs while constructing the graph which is particularly useful for several verification t...

We provide an approach to distribute the calculation of PageRank, by splitting the graph into its strongly connected components. As we prove, the global ranking may be calculated componentwise, as long as the rankings of pages directly linking to the current component are already known. Depending on the structure of the WWW, this approach approach may be used to calculate the ranking on several...

We present two improved versions of Tarjan's algorithm for the detection of strongly connected components in a directed graph. Our new algorithms handle sparse graphs and graphs with many trivial components (containing only one node) more economically than Tarjan's original algorithm. As an application we present an eecient transitive closure algorithm.

In this paper we investigate the organizational structure of the transcriptional regulatory network of S. cerevisiae with respect to the connectivity structure of periodic genes. We demonstrate that the giant strongly connected component plays a prominent role serving as central connector for genes experimentally found to be periodically expressed during the cell cycle of yeast. Numerically, we...

In this paper we present a CTL-like logic which is interpreted over the state spaces of Coloured Petri Nets. The logic has been designed to express properties of both state and transition information. This is possible because the state spaces are labelled transition systems. We compare the expressiveness of our logic with CTL’s. Then, we present a model checking algorithm which for efficiency r...