The real-time routing for satellite communication of the mega-constellations is being challenged due to the large-scale of network nodes, especially on devices with limited computation such as onboard embedded systems. In this paper, a fast routing method is proposed for mega-constellation backbone networks. Firstly, inspired by the regularity and sparse characteristics of mega-constellations, the 4-degree percolation theory is proposed to describe the node search process. Then, dynamic minimum search and mapping methods are used to narrow down the traversal range. The proposed method performs as well as the heap-optimized Dijkstra algorithm with less memory space and dynamic access. The experimental results show that the method proposed in this paper can significantly reduce routing computation time, especially on the onboard, edge-computing or other computation-limited devices.