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

Abstract

The time slot assignment problem (TSAP) or Satellite Communications scheduling problem (SCSP) for a satellite performs <TEX>$n{\times}n$</TEX> ground station data traffic switching has been known NP-hard problem. This paper suggests <TEX>$O(n^2)$</TEX> time complexity algorithm for TSAP of a satellite that performs <TEX>$n^2{\times}n^2$</TEX> ground station data traffic switching. This problem is more difficult than <TEX>$n{\times}n$</TEX> 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 <TEX>$D_{LB}$</TEX> traffic matrix that sum of rows and columns all of transponders have LB. Finally, we select the maximum traffic of row and column in <TEX>$D_{LB}$</TEX>, 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.