Polynomial Time Algorithm for Multi-Beam SS/TDMA Satellite Communications Scheduling Problem with Frequency-Hopping Ground Stations

The time slot assignment problem (TSAP) or Satellite Communications scheduling problem (SCSP) for a satellite performs $n{\times}n$ ground station data traffic switching has been known NP-hard problem. This paper suggests $O(n^2)$ time complexity algorithm for TSAP of a satellite that performs $n^2{\times}n^2$ ground station data traffic switching. This problem is more difficult than $n{\times}n$ TSAP as NP-hard problem. Firstly, we compute the average traffic for n-transponder's basic coverage zone and applies ground station exchange method that swap the ground stations until all of the transponders have a average value as possible. Nextly, we transform the D matrix to $D_{LB}$ traffic matrix that sum of rows and columns all of transponders have LB. Finally, we select the maximum traffic of row and column in $D_{LB}$, then decide the duration of kth switch mode to minimum traffic from selected values. The proposed algorithm can be get the optimal solution for experimental data.