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Rendl, F.

On the complexity of decomposing matrices arising in satellite communication. (English) Zbl 0569.90064

Oper. Res. Lett. 4, 5-8 (1985).
Decomposing a square matrix into a weighted sum of permutation matrices, such that the sum of the weights becomes minimal, is NP-hard. This result justifies the heuristic approach to this problem proposed by several authors. An application of this problem arises from intercity communication via transmission satellites.

Cited in 15 Documents

MSC:

90C10 Integer programming
90C90 Applications of mathematical programming
65K05 Numerical mathematical programming methods

Keywords:

computational complexity; communication matrices; matrix decomposition; Decomposing a square matrix; weighted sum of permutation matrices; heuristic; intercity communication; transmission satellites
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\textit{F. Rendl}, Oper. Res. Lett. 4, 5--8 (1985; Zbl 0569.90064)
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References:

[1] E. Balas and P.R. Landweer, “Traffic assignment in communication satellites”, OR Letters{\bf2}, 141-147. · Zbl 0526.90065
[2] Burkard, R.E., On the decomposition of traffic matrices arising in communication satellites, ()
[3] Camerini, P.; Maffioli, F.; Tartara, P., Some scheduling algorithms for SS/TDMA systems, (), 405-409
[4] Frieze, A.M., Complexity of a 3-dimensional assignment problem, European journal of operational research, 13, 161-164, (1983) · Zbl 0507.90057
[5] Garey, M.K.; Johnson, D.S., Computers and intractability: A guide to the theory of NP - completeness, (1979), Freeman San Francisco, CA · Zbl 0411.68039
[6] Inukai, T., An efficient SS/TDMA time slot assignment algorithm, IEEE transactions on communications, 27, 1449-1455, (1979)
[7] Rendl, F., On the complexity of decomposing matrices arising in satellite communication, () · Zbl 0569.90064
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.