pcds (version 0.1.2)

PEdom1D: The domination number of Proportional Edge Proximity Catch Digraph (PE-PCD) for 1D data

Description

Returns the domination number of PE-PCD whose vertices are the 1D data set Xp.

Yp determines the end points of the intervals (i.e., partition the real line via intervalization).

PE proximity region is constructed with expansion parameter \(r \ge 1\) and centrality parameter \(c \in (0,1)\).

Usage

PEdom1D(Xp, Yp, r, c = 0.5)

Arguments

Xp

A set of 1D points which constitute the vertices of the PE-PCD.

Yp

A set of 1D points which constitute the end points of the intervals which partition the real line.

r

A positive real number which serves as the expansion parameter in PE proximity region; must be \(\ge 1\).

c

A positive real number in \((0,1)\) parameterizing the center inside int (default c=.5).

Value

A list with two elements

dom.num

Domination number of PE-PCD with vertex set = Xp and expansion parameter \(r \ge 1\) and centrality parameter \(c \in (0,1)\).

mds

A minimum dominating set of PE-PCD with vertex set = Xp and expansion parameter \(r \ge 1\) and centrality parameter \(c \in (0,1)\).

See Also

PEdomMTnd

Examples

# NOT RUN {
a<-0; b<-10; int<-c(a,b)
c<-.4
r<-2

#nx is number of X points (target) and ny is number of Y points (nontarget)
nx<-20; ny<-4;  #try also nx<-40; ny<-10 or nx<-1000; ny<-10;

set.seed(1)
Xp<-runif(nx,a,b)
Yp<-runif(ny,a,b)

plotIntervals(Xp,Yp,main="Xp Points and Intervals Based on Yp Points")
plotPEregsMI(Xp,Yp,r,c,main="PE Proximity Regions for Xp points - Intervalization is by Yp Points")

PEdom1D(Xp,Yp,r,c)

PEdom1D(Xp,Yp,r,c=.25)
PEdom1D(Xp,Yp,r,c=.01)
PEdom1D(Xp,Yp,r=1.25,c)

# }