  In this paper, the routing in massive low earth orbit (LEO) satellite
networks is studied. When the satellite-to-satellite communication distance is
limited, we choose different relay satellites to minimize the latency in a
constellation at a constant altitude. Firstly, the global optimum solution is
obtained in the ideal scenario when there are available satellites at all the
ideal locations. Next, we propose a nearest neighbor search algorithm for
realistic (non-ideal) scenarios with a limited number of satellites. The
proposed algorithm can approach the global optimum solution under an ideal
scenario through a finite number of iterations and a tiny range of searches.
Compared with other routing strategies, the proposed algorithm shows
significant advantages in terms of latency. Furthermore, we provide two
approximation techniques that can give tight lower and upper bounds for the
latency of the proposed algorithm, respectively. Finally, the relationships
between latency and constellation height, satellites' number, and communication
distance are investigated.
