A polynomial time optimal algorithm for satellite communications with general switching modes

The Satellite-Switched Time-Division Multiple Access (SS /TDMA) is a technique effectively used in wideband communication satellites. A very important problem for SS/TDMA systems is the proper communications scheduling over the satellite equipment. This problem is equivalent to decomposing a given traffic matrix T into a positive linear combination of $( 0,1 )$-matrices satisfying additional technology-dependant constraints. The sum of the multiplying constants represents the time taken by the satellite to handle the communications and must be minimum in order to achieve an efficient use of the equipment. A polynomial time optimal algorithm for the SS/TDMA scheduling problem for systems with variable bandwidth beams and restricted multiplexing and demultiplexing is presented. As a corollary of the presented results, another generalization of the classical Birkhoff-von Neumann Theorem is established.