Graph Reachability on Parallel Many-Core Architectures

Many modern applications are modeled using graphs of some kind. Given a graph, reachability, that is, discovering whether there is a path between two given nodes, is a fundamental problem as well as one of the most important steps of many other algorithms. The rapid accumulation of very large graphs (up to tens of millions of vertices and edges) from a diversity of disciplines demand efficient and scalable solutions to the reachability problem. General-purpose computing has been successfully used on Graphics Processing Units (GPUs) to parallelize algorithms that present a high degree of regularity. In this paper, we extend the applicability of GPU processing to graph-based manipulation, by re-designing a simple but efficient state-of-the-art graph-labeling method, namely the GRAIL (Graph Reachability Indexing via RAndomized Interval) algorithm, to many-core CUDA-based GPUs. This algorithm firstly generates a label for each vertex of the graph, then it exploits these labels to answer reachability queries. Unfortunately, the original algorithm executes a sequence of depth-first visits which are intrinsically recursive and cannot be efficiently implemented on parallel systems. For that reason, we design an alternative approach in which a sequence of breadth-first visits substitute the original depth-first traversal to generate the labeling, and in which a high number of concurrent visits is exploited during query evaluation. The paper describes our strategy to re-design these steps, the difficulties we encountered to implement them, and the solutions adopted to overcome the main inefficiencies. To prove the validity of our approach, we compare (in terms of time and memory requirements) our GPU-based approach with the original sequential CPU-based tool. Finally, we report some hints on how to conduct further research in the area.

Implicit Landmark Path Indexing for Bounded Label Constrained Reachable Paths

In today’s Big Data era, a graph is an essential tool that models the semi-structured or unstructured data. Graph reachability with vertex or edge constraints is one of the basic queries to extract useful information from the graph data. From the graph reachability with constraints, we obtained the information about the existence of a path between the given two vertices satisfying the vertex or edge constraints. The problem of Label Constraint Reachability (LCR) found the existence of a path between the two given vertices such that the edge-labels along the path are the subset of the given edge-label constraint. We extended the LCR queries by considering weighted directed graphs and proposed a novel technique of finding paths for LCR queries bounded by path weight. We termed these paths as bounded label constrained reachable paths (BLCRP). We extended the landmark path indexing technique [1] by incorporating the implicit paths which satisfy the user constraints but need not satisfy the minimality of edge label sets. We solved the BLCRP by using the extended landmark path indexing and BFS based query processing. We addressed the following challenges through our proposed technique of implicit landmark path indexing in the problem of BLCRP that included (1) the need to handle exponential number of edge label combinations with an additional total path weight constraint, and (2) the need to discover a technique that finds exact reachable paths between the given vertices. This problem could be applied to real network scenarios like road networks, social networks, and proteinprotein interaction networks. Our experiments and statistical analysis revealed the accuracy and efficiency of the proposed approach tested on synthetic and real datasets.

Algorithm for Identifying Minimum Driver Nodes Based on Structural Controllability

Existing methods on structural controllability of networked systems are based on critical assumptions such as nodal dynamics with infinite time constants and availability of input signals to all nodes. In this paper, we relax these assumptions and examine the structural controllability for practical model of networked systems. We explore the relationship between structural controllability and graph reachability. Consequently, a simple graph-based algorithm is presented to obtain the minimum driver nodes. Finally, simulation results are presented to illustrate the performance of the proposed algorithm in dealing with large-scale networked systems.