Broadcast graph: различия между версиями

Материал из WEGA
Перейти к навигации Перейти к поиску
(Новая страница: «'''Broadcast graph''' --- граф широковещания. Let us first consider the full-duplex model (See ''Broadcasting problem''.) Let <math>G</math> be a …»)
 
Нет описания правки
 
Строка 1: Строка 1:
'''Broadcast graph''' --- граф широковещания.  
'''Broadcast graph''' — ''[[граф широковещания]].''


Let us first consider the
Let us first consider the full-duplex model (See ''[[Broadcasting problem]]''.) Let <math>\,G</math> be a [[graph, undirected graph, nonoriented graph|graph]] modeling an interconnection [[network]]. We will denote by <math>\,b(v)</math> the broadcast time of <math>\,v</math>, that is the
full-duplex model (See ''Broadcasting problem''.) Let <math>G</math> be a graph modeling an interconnection
time to achieve broadcasting from a [[vertex]] <math>\,v</math> of <math>\,G</math> in the network.
network. We will denote by <math>b(v)</math> the broadcast time of <math>v</math>, that is the
time to achieve broadcasting from a vertex <math>v</math> of <math>G</math> in the network.
Moreover, <math>b(G)</math>, the broadcast time of <math>G</math>, is defined as follows:
Moreover, <math>b(G)</math>, the broadcast time of <math>G</math>, is defined as follows:


<math>b(G) = \max\{b(v)| \; v \in V(G)\}.</math>
:::::<math>b(G) = \max\{b(v)| \; v \in V(G)\}.</math>


If we consider a complete graph of order <math>n</math>, <math>K_{n}</math>, it is not
If we consider a [[complete graph]] of order <math>\,n</math>, <math>\,K_{n}</math>, it is not
difficult to see that <math>b(K_{n}) = \lceil\log_{2}(n)\rceil</math>. Any graph
difficult to see that <math>b(K_{n}) = \lceil\log_{2}(n)\rceil</math>. Any graph
<math>G</math> such that <math>b(G) = b(K_{n}) = \lceil\log_{2}(n)\rceil</math> is called a
<math>G</math> such that <math>b(G) = b(K_{n}) = \lceil\log_{2}(n)\rceil</math> is called a
'''broadcast graph'''. We call a '''minimum broadcast graph''' of order <math>n</math> any
'''broadcast graph'''. We call a '''[[minimum broadcast graph]]''' of order <math>\,n</math> any
broadcast graph <math>G</math> having the minimum number of edges. This number is
broadcast graph <math>\,G</math> having the minimum number of [[edge|edges]]. This number is
denoted by <math>B(n)</math>.
denoted by <math>\,B(n)</math>.


Similarly, a '''broadcast digraph''' is defined, using the
Similarly, a '''broadcast digraph''' is defined, using the half-duplex model.
half-duplex model.
 
==Литература==
 
* Евстигнеев В.А., Касьянов В.Н. Словарь по графам в информатике. — Новосибирск: Сибирское Научное Издательство, 2009.

Текущая версия от 16:31, 23 октября 2018

Broadcast graphграф широковещания.

Let us first consider the full-duplex model (See Broadcasting problem.) Let [math]\displaystyle{ \,G }[/math] be a graph modeling an interconnection network. We will denote by [math]\displaystyle{ \,b(v) }[/math] the broadcast time of [math]\displaystyle{ \,v }[/math], that is the time to achieve broadcasting from a vertex [math]\displaystyle{ \,v }[/math] of [math]\displaystyle{ \,G }[/math] in the network. Moreover, [math]\displaystyle{ b(G) }[/math], the broadcast time of [math]\displaystyle{ G }[/math], is defined as follows:

[math]\displaystyle{ b(G) = \max\{b(v)| \; v \in V(G)\}. }[/math]

If we consider a complete graph of order [math]\displaystyle{ \,n }[/math], [math]\displaystyle{ \,K_{n} }[/math], it is not difficult to see that [math]\displaystyle{ b(K_{n}) = \lceil\log_{2}(n)\rceil }[/math]. Any graph [math]\displaystyle{ G }[/math] such that [math]\displaystyle{ b(G) = b(K_{n}) = \lceil\log_{2}(n)\rceil }[/math] is called a broadcast graph. We call a minimum broadcast graph of order [math]\displaystyle{ \,n }[/math] any broadcast graph [math]\displaystyle{ \,G }[/math] having the minimum number of edges. This number is denoted by [math]\displaystyle{ \,B(n) }[/math].

Similarly, a broadcast digraph is defined, using the half-duplex model.

Литература

  • Евстигнеев В.А., Касьянов В.Н. Словарь по графам в информатике. — Новосибирск: Сибирское Научное Издательство, 2009.