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1982 | 10 | 19 |
Tytuł artykułu

The theorems of Koenig and Birkhoff and their connection with the minimization of the duration time of the measurements of automatic telecommunication channels

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EN
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PL
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EN
A problem (P) of minimization of the duration time of the measurements of automatic telecommunication channels is considered. P is a discrete optimization problem solved by graph theory methods. It is defined by (i)-(v), where: (i) for each i, 1≤i≤p, and j, 1≤1≤p, there are given k ij channels to be measured between node ”i” and node ”j”; (ii) measurement of one channel lasts one unit; (iii) there are exactly two devices, say A, B, in each node (the case where there is an arbitrary number of devices A, B in each node may be easily reduced to this case); (iv) the channel between node ”i” and node ”j” may be measured only by use of device A being present in node ”i” and device B in node ”j”; (v) in each time both devices A or B may measure only one channel. To solve P, some knowledge of hypergraphs as well as functional analysis (the Krein-Milman theorem) and linear algebra (the Koenig theorem) is necessary. The Koenig theorem is proved in a simple manner similarly as the dual Koenig theorem (which is a new result). As corollaries the Birkhoff theorem about bistochastic matrices and the dual Birkhoff theorem are deduced.
Rocznik
Tom
10
Numer
19
Opis fizyczny
Daty
wydano
1982
online
1982-02-01
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Bibliografia
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.ojs-doi-10_14708_ma_v10i19_1532
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