The existing distributed triangle counting algorithms assume that all computing nodes are in the same location, while in reality, the nodes may be located in multiple data centers across continents. Geo-distributed data centers which are connected with wide area networks have characteristics of heterogeneous network bandwidth, high communication cost and uneven distribution, and the existing distributed algorithms cannot be applied to geo-distributed environment. At the same time, the existing research which ignores the temporal locality of the formation of triangles mostly adopts strategies such as random sampling and elimination of edges. Therefore, the triangle counting problem of real graph streams in geo-distributed environment was studied, and a Geo-distributed Triangle Counting (GTC) algorithm was proposed. Firstly, aiming at the problem of too high data transmission caused by the existing edge distribution strategy, a geo-distributed edge distribution strategy was proposed to build a benefit formula combining the time benefit and data benefit of communication and use point-to-point communication to replace broadcast edges. Then, for the triangle repeated counting problem caused by point-to-point communication in geo-distributed environment, a final edge calculation rule was proposed to ensure no counting repetition. Finally, based on the time weighted sampling algorithm, a time-weighted triangle counting algorithm was proposed to use the time locality of the triangle to sample. The GTC was compared with Conditional Counting and Sampling (CoCoS) and Tri-Fly on five real graph streams. The results show that GTC has the communication data size decreased by 17% compared to CoCoS and decreased by 44% compared to Tri-Fly, GTC has the error rate decreased by 53% compared to Tri-Fly and slightly less than CoCoS, and GTC has the running time decreased by 34% compared to Tri-Fly and slightly more than CoCoS. It can be seen that the GTC can reduce the size of communication data effectively while ensuring high accuracy and short algorithm running time.
Attributed graph embedding aims to represent the nodes in an attributed graph into low-dimensional vectors while preserving the topology information and attribute information of the nodes. There are lots of works related to attributed graph embedding. However, most of algorithms proposed in them are supervised or semi-supervised. In practical applications, the number of nodes that need to be labeled is large, which makes these algorithms difficult and consume huge manpower and material resources. Above problems were reanalyzed from an unsupervised perspective, and an unsupervised attributed graph embedding algorithm was proposed. Firstly, the topology information and attribute information of the nodes were calculated respectively by using the existing non-attributed graph embedding algorithm and attributes of the attributed graph. Then, the embedding vector of the nodes was obtained by using Graph Convolutional Network (GCN), and the difference between the embedding vector and the topology information and the difference between the embedding vector and attribute information were minimized. Finally, similar embeddings was obtained by the paired nodes with similar topological information and attribute information. Compared with Graph Auto-Encoder (GAE) method, the proposed method has the node classification accuracy improved by 1.2 percentage points and 2.4 percentage points on Cora and Citeseer datasets respectively. Experimental results show that the proposed method can effectively improve the quality of the generated embedding.
In order to improve the energy efficiency of the heterogeneous wireless networks with macro-cells and micro-cells, a Joint Switch scheduling and Resource Allocation (JSRA) algorithm was proposed. Firstly, based on sleeping of micro base stations, Centralized User Switch scheduling Algorithm (CUSA) was adopted to determine the associated base station for each user. The sleeping/waking status of a micro base station was judged according to whether to decrease of network power consumption when users of the micro base station entirely switched to macro base station.Then, the Best Channel quality Subcarrier Adjustment (BCSA) algorithm was used to assign subcarriers and transmission power for users. The network energy efficiency was guaranteed to approximate the optimal solution by adjusting the subcarrier allocation between the user with the maximum energy efficiency and the user with the minimum energy efficiency. The theoretical analysis and simulation experiments show that,compared with three existing algorithms which considered user handoff or resource allocation separately, JSRA has high computational complexity; however, when the number of users is 120, JSRA can reduce network power consumption 44.4% at most, increase the total effective data rate of users by 80% with the slight reduction only than one contrast as well as the energy efficiency of the network by 200% at most. Experimental results show JSRA can improve the energy efficiency of heterogeneous wireless networks effectively.