A heuristic for decomposing traffic matrices in TDMA satellite communication

A heuristic for decomposing traffic matrices in TDMA satellite communication. With the time-division multiple access (TDMA) technique in satellite communication the problem arises to decompose a given n x n tramc matrix into a weighted sum of a small number of permutation matrices such that the sum of the weights becomes minimal. There are polynomial algorithms when the number of permutation matrices in a decomposition is allowed to be as large as n 2. When the number of matrices is restricted to n, the problem is NP-hard. In this paper we propose a heuristic based on a scaling technique which for each number of allowed matrices in the range from n to n 2 allows to give a performance guarantee with respect to the total weight of the solution. As a subroutine we use new heuristic methods for decomposing a matrix of small integers into as few matrices as possible without exceeding the lower bound on the total weight. Computational results indicate that the method might also be practical. Key~ Words: Matrix decomposition problem, TDMA satellite communication, greedy heuristics, edge coloring, bottleneck assignment problem, voting systems, apportionment.