The traffic scheduling problem for a satellite cluster with an arbitrary number of satellites is considered. which is one of the most interesting problems in the satellite communication scheduling area. This problem is to find a time slot assignment maximizing the transponder utilization for a satellite cluster This problem is known to be NP-complete, and several heuristic algorithms have been proposed. In this paper, we suggest new efficient algorithms for this problem, which have less time complexity than the best existing one and provide much better solution quality. Extensive simulation results are reported.