Pointer Network Based Deep Learning Algorithm for the Maximum Clique Problem

The maximum clique problem (MCP) is a famous NP-hard problem, which is difficult for the exact algorithm to solve when the dimension is large. In this paper, we applied the pointer network based method to solve this problem. First, we illustrated how to train the network with supervised learning strategy to obtain the solution to the maximum clique problem. We then further trained the pointer network with reinforcement learning strategy to obtain the vertices from the graph. For both strategies, backtracking algorithm is used to reselect the vertices. From the experimental results, we can see that both supervised learning and reinforcement learning work well. Promising results can be obtained up to 100 dimensions. This illustrates that the deep neural network based algorithms have great potentials for solving the maximum clique problem effectively and efficiently.