pcds (version 0.1.8)

PEdom.num.tetra: The domination number of Proportional Edge Proximity Catch Digraph (PE-PCD) - one tetrahedron 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 tetrahedron th with expansion parameter \(r \ge 1\) and vertex regions are based on the center M which is circumcenter ("CC") or center of mass ("CM") of th with default="CM".

See also (ceyhan:Phd-thesis,ceyhan:comp-geo-2010;textualpcds).

Usage

PEdom.num.tetra(Xp, th, r, M = "CM")

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 3D points which constitute the vertices of the digraph.

th

A \(4 \times 3\) matrix with each row representing a vertex of the tetrahedron.

r

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

M

The center to be used in the construction of the vertex regions in the tetrahedron, th. Currently it only takes "CC" for circumcenter and "CM" for center of mass; default="CM".

Author

Elvan Ceyhan

References

See Also

PEdom.num.tri

Examples

# \donttest{
A<-c(0,0,0); B<-c(1,0,0); C<-c(1/2,sqrt(3)/2,0); D<-c(1/2,sqrt(3)/6,sqrt(6)/3)
tetra<-rbind(A,B,C,D)
n<-10  #try also n<-20

Xp<-runif.tetra(n,tetra)$g

M<-"CM"  #try also M<-"CC"
r<-1.25

PEdom.num.tetra(Xp,tetra,r,M)

P1<-c(.5,.5,.5)
PEdom.num.tetra(P1,tetra,r,M)
# }