SS/TDMA Time Slot Assignment with Restricted Switching Modes

Lewandowski, J. L.; Liu, J.; Liu, C.

doi:10.1109/tcom.1983.1095734

Cited by 37 publications

(8 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The currently best heuristic for decomposing into n matrices is due to Balas and Landweer (1983). Decomposing into a number q of matrices which is slightly larger than n has also been considered, for example by Lewandowski, Liu, and Liu (1983), who decompose into 2n matrices (which are given in advance), cf. also Burkard (1985), section 4.…”

Section: Related Resultsmentioning

confidence: 99%

“…The problem treated by Ribeiro, Minoux, and Penna (1989) is also similar; -duration-optimal decomposition, e.g., Inukai (1979), Burkard (1985); -decomposition with a small set (usually about 2n) of permutation matrices which are given in advance, see Lewandowski, Liu, and Liu (1983).…”

Section: Resultsmentioning

confidence: 99%

“…In fact, it is nothing but the original problem with a restricted set of permutation matrices. (Lewandowski, Liu, and Liu (1983) and Burkard (1985) have considered the case of 2n given permutation matrices which correspond to a pair of orthogonal Latin squares. In this case the linear program has a special structure which can be used.)…”

Section: Step (D): Adjusting the Solutionmentioning

confidence: 99%

See 2 more Smart Citations

A heuristic for decomposing traffic matrices in TDMA satellite communication

Rote

Vogel

1993

ZOR - Methods and Models of Operations Research

View full text Add to dashboard Cite

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.

show abstract

Section: Related Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Section: Step (D): Adjusting the Solutionmentioning

confidence: 99%

See 1 more Smart Citation

A heuristic for decomposing traffic matrices in TDMA satellite communication

Rote

Vogel

1993

ZOR - Methods and Models of Operations Research

View full text Add to dashboard Cite

show abstract

“…Lewandowski et al [1983] describe an algorithm for this problem, which solves it in 0 (n 7/2 log t) steps, where t is the largest entry in the traffic matrix T. We shall show in the following that problem (4.3) and (4.4) can be transformed to a classical assignment problem and is therefore solvable by a genuinely polynomial algorithm in O (n3)-time. According to a theorem of Heller and Tompkins [1958] the matrix occurring in the constraint set (4.6) is totally unimodular.…”

Section: Decomposition In 2 N Fixed Switch Modesmentioning

confidence: 99%

Time-slot assignment for TDMA-systems

Burkard

1985

Computing

View full text Add to dashboard Cite

--ZusammenfassungTime-Slot Assignment for TDMA-Systems. In satellite communication as in other technical systems using the TDMA-technique (time division multiple access) the problem arises to decompose a given (n • n)-matrix in a weighted sum of permutation matrices such that the sum of the weights becomes minimal. We show at first that an optimal solution of this problem can be obtained in O (n4)-time using at most O (n 2) different permutation matrices. Thereafter we discuss shortly the decomposition in O (n) different matrices which turns out to be NP-hard. 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. AMS Subject Classifications:90C08, 90C 10.

show abstract

“…In [23] the problem of finding a solution when n transponders are present and an n × n demand matrix is given is studied under the particular restriction that only a restricted set of switching matrices can be used. In such a case, of course, the authors notice that linear programming can minimize the total transfer time, which means that the solution of the problem can be found efficiently.…”

Section: Related Workmentioning

confidence: 99%