Maintenance of Strongly Connected Component in Shared-memory Graph

In this paper, we present an on-line fully dynamic algorithm for maintaining strongly connected component of a directed graph in a shared memory architecture. The edges and vertices are added or deleted concurrently by fixed number of threads. To the best of our knowledge, this is the first work to propose using linearizable concurrent directed graph and is build using both ordered and unordered list-based set. We provide an empirical comparison against sequential and coarse-grained. The results show our algorithm's throughput is increased between 3 to 6x depending on different workload distributions and applications. We believe that there are huge applications in the on-line graph. Finally, we show how the algorithm can be extended to community detection in on-line graph.Comment: 29 pages, 4 figures, Accepted in the Conference NETYS-201

Efficient Dynamic Approximate Distance Oracles for Vertex-Labeled Planar Graphs

Let $G$ be a graph where each vertex is associated with a label. A Vertex-Labeled Approximate Distance Oracle is a data structure that, given a vertex $v$ and a label $\lambda$, returns a $(1+\varepsilon)$-approximation of the distance from $v$ to the closest vertex with label $\lambda$ in $G$. Such an oracle is dynamic if it also supports label changes. In this paper we present three different dynamic approximate vertex-labeled distance oracles for planar graphs, all with polylogarithmic query and update times, and nearly linear space requirements

Finding 2-Edge and 2-Vertex Strongly Connected Components in Quadratic Time

We present faster algorithms for computing the 2-edge and 2-vertex strongly connected components of a directed graph, which are straightforward generalizations of strongly connected components. While in undirected graphs the 2-edge and 2-vertex connected components can be found in linear time, in directed graphs only rather simple $O(m n)$-time algorithms were known. We use a hierarchical sparsification technique to obtain algorithms that run in time $O(n^2)$. For 2-edge strongly connected components our algorithm gives the first running time improvement in 20 years. Additionally we present an $O(m^2 / \log{n})$-time algorithm for 2-edge strongly connected components, and thus improve over the $O(m n)$ running time also when $m = O(n)$. Our approach extends to k-edge and k-vertex strongly connected components for any constant k with a running time of $O(n^2 \log^2 n)$ for edges and $O(n^3)$ for vertices

CellExcite: an efficient simulation environment for excitable cells

Background Brain, heart and skeletal muscle share similar properties of excitable tissue, featuring both discrete behavior (all-or-nothing response to electrical activation) and continuous behavior (recovery to rest follows a temporal path, determined by multiple competing ion flows). Classical mathematical models of excitable cells involve complex systems of nonlinear differential equations. Such models not only impair formal analysis but also impose high computational demands on simulations, especially in large-scale 2-D and 3-D cell networks. In this paper, we show that by choosing Hybrid Automata as the modeling formalism, it is possible to construct a more abstract model of excitable cells that preserves the properties of interest while reducing the computational effort, thereby admitting the possibility of formal analysis and efficient simulation. Results We have developed CellExcite, a sophisticated simulation environment for excitable-cell networks. CellExcite allows the user to sketch a tissue of excitable cells, plan the stimuli to be applied during simulation, and customize the diffusion model. CellExcite adopts Hybrid Automata (HA) as the computational model in order to efficiently capture both discrete and continuous excitable-cell behavior. Conclusions The CellExcite simulation framework for multicellular HA arrays exhibits significantly improved computational efficiency in large-scale simulations, thus opening the possibility for formal analysis based on HA theory. A demo of CellExcite is available at http://www.cs.sunysb.edu/~eha/ webcite

Short Paper: Maintenance of Strongly Connected Component in Shared-Memory Graph

In this paper, we present an on-line fully dynamic algorithm for maintaining strongly connected component of a directed graph in a shared memory architecture. The edges and vertices are added or deleted concurrently by fixed number of threads. To the best of our knowledge, this is the first work to propose using linearizable concurrent directed graph and is build using both ordered and unordered list-based set. We provide an empirical comparison against sequential and coarse-grained. The results show our algorithm’s throughput is increased between 3 to 6x depending on different workload distributions and applications. We believe that there are huge applications in the on-line graph. Finally, we show how the algorithm can be extended to community detection in on-line graph

A Theoretical Study of a Generalized Version of Kleinberg's HITS Algorithm

Kleinberg's HITS algorithm (Kleinberg 1999), which was originally developed in a Web context, tries to infer the authoritativeness of a Web page in relation to a specific query using the structure of a subgraph of the Web graph, which is obtained considering this specific query. Recent applications of this algorithm in contexts far removed from that of Web searching (Bacchin, Ferro and Melucci 2002, Ng et al. 2001) inspired us to study the algorithm in the abstract, independently of its particular applications, trying to mathematically illuminate its behaviour. In the present paper we detail this theoretical analysis. The original work starts from the definition of a revised and more general version of the algorithm, which includes the classic one as a particular case. We perform an analysis of the structure of two particular matrices, essential to studying the behaviour of the algorithm, and we prove the convergence of the algorithm in the most general case, finding the analytic expression of the vectors to which it converges. Then we study the symmetry of the algorithm and prove the equivalence between the existence of symmetry and the independence from the order of execution of some basic operations on initial vectors. Finally, we expound some interesting consequences of our theoretical results