pcds (version 0.1.6)

PEdomTri: The domination number of Proportional Edge Proximity Catch Digraph (PE-PCD) - one triangle case

Description

Returns the domination number of PE-PCD whose vertices are the data points in Xp.

PE proximity region is defined with respect to the triangle tri with expansion parameter \(r \ge 1\) and vertex regions are constructed with center \(M=(m_1,m_2)\) in Cartesian coordinates or \(M=(\alpha,\beta,\gamma)\) in barycentric coordinates in the interior of the triangle tri or the circumcenter of tri.

See also (ceyhan:Phd-thesis,ceyhan:masa-2007,ceyhan:dom-num-NPE-Spat2011,ceyhan:mcap2012;textualpcds).

Usage

PEdomTri(Xp, tri, r, M = c(1, 1, 1))

Value

A list with two elements

dom.num

Domination number of PE-PCD with vertex set = Xp and expansion parameter \(r \ge 1\) and center M

mds

A minimum dominating set of PE-PCD with vertex set = Xp and expansion parameter \(r \ge 1\) and center M

ind.mds

Indices of the minimum dominating set mds

Arguments

Xp

A set of 2D points which constitute the vertices of the digraph.

tri

A \(3 \times 2\) matrix with each row representing a vertex of the triangle.

r

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

M

A 2D point in Cartesian coordinates or a 3D point in barycentric coordinates which serves as a center in the interior of the triangle tri or the circumcenter of tri which may be entered as "CC" as well; default is \((1,1,1)\) i.e., the center of mass.

Author

Elvan Ceyhan

References

See Also

PEdom.nd, PEdom and PEdom1D

Examples

if (FALSE) {
A<-c(0,0); B<-c(1,0); C<-c(1/2,sqrt(3)/2)
Tr<-rbind(A,B,C)
n<-10  #try also n<-20
Xp<-runif.tri(n,Tr)$g

M<-as.numeric(runif.tri(1,Tr)$g)  #try also M<-c(1,1,1)

r<-1.4

PEdomTri(Xp,Tr,r,M)
IM<-IncMatPEtri(Xp,Tr,r,M)
dom.greedy #try also dom.exact(IM)

gr.gam<-dom.greedy(IM)
gr.gam
Xp[gr.gam$i,]

PEdomTri(Xp,Tr,r,M=c(.4,.4))
}