This paper reviews the sequential, parallel and distributed implementations of strongly connected component algorithms, and analyzes the challenges of each implementation in the graph iteration paradigm of distributed processing. We also review the graph data layout and communication mode of each distributed graph processing system, and analyze the defect of high memory usage in the implementation of the strongly connected component algorithm of the existing distributed graph processing system. Therefore, we propose a strongly connected component algorithm that performs pull mode communication on CSR instead of traversing the transposed graph. Experiments show that the memory consumption of our method is greatly reduced, and the running time of the algorithm is much lower than that of the most advanced implementation. On four publicly accessible data sets, our approach reduces computation time and storage space by an average of 26% and 39%, respectively. In addition, we optimize the general pull communication mode, resulting in 15.2°/0 computation time reduction on the four publicly available data sets.

Graph is often used for data analysis. Distributed graph processing is gaining traction as it becomes more difficult for a single machine to store and process the complete graph due to the growing volume of data. We investigated 26 popular distributed graph processing systems and the graph algorithms and datasets provided by these systems. The computational logic of these graph algorithms does not distinguish between the types of vertices and edges, so distributed graph processing systems treat all vertices and edges in an undifferentiated way. However, using the hidden data connections of different types of vertices in multi-networks can greatly improve the accuracy of the community search algorithm. So we describe the challenges for the existing distributed graph processing systems to deal with different types of vertices and edges in multi-networks, and propose an index-based multi-network storage abstraction to store various vertices and edges, and a heuristic greedy algorithm to complete the partition job for different vertices and edges. Base on the two jobs, we finish the research of efficient community search for distributed graph processing in multi-networks, making it possible for future research of more algorithms for distributed graph processing in multi-networks.

In this paper, we consider the small cell range expansion problem in massive multiple-input multiple-output (MIMO) heterogeneous networks (HetNets) with limited backhaul capacity, and derive the close-form formulas to calculate the range expansion bias (REB) of equal uplink received signal strengths (RSSs) boundary (EUB). In order to reduce the effect of severe downlink intercell interference in the expanded regions (ERs) of small cell, we propose a downlink precoding scheme based on the estimated channel state information (CSI). Simulation results verify the relationships among different small cell coverage boundaries, and demonstrate the benefits of the proposed downlink precoding scheme in maximizing the overall sum rate and improving the performance of MIMO HetNets.