A Streaming Graph Partitioning Method to Achieve High Cohesion and Equilibrium via Multiplayer Repeated Game

With the advent of 5G era, Internet-of-Things will become possible, and a large amount of correlative data, namely the streaming graph (SG), is continuously generated in various application fields, which poses a great challenge to analyze and make good use of such graph data. The balanced partition of a big graph, especially a dynamic SG, has always been basic research in graph theory, and there are many classical methods. However, this article explores a novel method, that is, an SG
$k$
-way partitioning via a multiplayer repeated game so as to realize the equilibrium of the total number of nodes in different partitions and achieve high cohesion or low edge-cut in each partition. We regard the SG partitioning process during each time window as a multiplayer game process, treat
$k$
target partitions as game players, and use all possible actions that players select new nodes as the strategy set. Some effective constraints are given to reduce the strategy space and accelerate the game process. Moreover, we define equilibrium degree (ED) and modularity degree (MD), which are used to design the utility function of game players. All game players finally reach the Nash equilibrium via multiplayer repeated games. At this time, each player corresponds to a strategy. Under the guidance of these strategies, the new nodes are added to each target partition, and then the goal of optimal partitioning is achieved. The above operations are carried out in each time window. The subsequent time windows can reuse the partitioning results of the previous time window in order to realize dynamic incremental partitioning for an SG. Extensive experiments indicate that while ensuring the partition quality of an SG, our proposed algorithm also greatly improves the speed of online partitioning. Even compared with the state-of-the-art SG partitioning algorithm PLDG, our algorithm still obtains better performance.