Timeslot assignment for TDMAsystems
Abstract
In satellite communication as in other technical systems using the TDMAtechnique (time division multiple access), the problem arises to decompose a given (n x n)matrix in a weighted sum of permutation matrices such that the sum of the weights becomes minimal. It is shown at first that an optimal solution of this problem can be obtained in O (n exp 4)time using at most O (nsquared) different permutation matrices. Thereafter a short discussion in given of the decomposition in O(n) different matrices which turns out to be NPhard. Moreover, it is shown that an optimal decomposition using a class of 2 n permutation matrices which are fixed in advance can be obtained by solving a classical assignment problem. This latter problem can be generalized by taking arbitrary Boolean matrices. The corresponding decomposition problem can be transformed to a special max flow min cost network flow problem, and is thus soluble by a genuinely polynomial algorithm.
 Publication:

Computing
 Pub Date:
 1985
 Bibcode:
 1985Compu..35...99B
 Keywords:

 Matrix Theory;
 Time Division Multiple Access;
 Boolean Algebra;
 Linear Programming;
 Network Analysis;
 Permutations;
 Satellite Communication;
 Weighting Functions;
 Communications and Radar