Idom.setAStri {pcds}

The indicator for the set of points S being a dominating set or not for Arc Slice Proximity Catch Digraphs (AS-PCDs) - one triangle case

Description

Returns I(S a dominating set of AS-PCD), that is, returns 1 if S is a dominating set of AS-PCD, returns 0 otherwise.

AS-PCD has vertex set Xp and AS proximity region is constructed with vertex regions are based on the 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 based on circumcenter of tri; default is M="CC", i.e., circumcenter of tri whose vertices are also labeled as edges 1, 2, and 3, respectively.

See also (Ceyhan (2005, 2010)).

Usage

Idom.setAStri(S, Xp, tri, M = "CC")

Arguments

S

A set of 2D points which is to be tested for being a dominating set for the AS-PCDs.

Xp

A set of 2D points which constitute the vertices of the AS-PCD.

tri

Three 2D points, stacked row-wise, each row representing a vertex of the triangle.

M

The center of the triangle. "CC" stands for circumcenter of the triangle tri or a 2D point in Cartesian coordinates or a 3D point in barycentric coordinates which serves as a center in the interior of tri; default is M="CC" i.e., the circumcenter of tri.

Value

I(S a dominating set of AS-PCD), that is, returns 1 if S is a dominating set of AS-PCD whose vertices are the data points in Xp; returns 0 otherwise, where AS proximity region is constructed in the triangle tri.

Author(s)

Elvan Ceyhan

References

Ceyhan E (2005). An Investigation of Proximity Catch Digraphs in Delaunay Tessellations, also available as technical monograph titled Proximity Catch Digraphs: Auxiliary Tools, Properties, and Applications. Ph.D. thesis, The Johns Hopkins University, Baltimore, MD, 21218.

Ceyhan E (2010). “Extension of One-Dimensional Proximity Regions to Higher Dimensions.” Computational Geometry: Theory and Applications, 43(9), 721-748.

Ceyhan E (2012). “An investigation of new graph invariants related to the domination number of random proximity catch digraphs.” Methodology and Computing in Applied Probability, 14(2), 299-334.

See Also

IarcASset2pnt.tri, Idom.setPEtri and Idom.setCStri

Examples

A<-c(1,1); B<-c(2,0); C<-c(1.5,2);

Tr<-rbind(A,B,C);
n<-10

set.seed(1)
Xp<-runif.tri(n,Tr)$gen.points

M<-as.numeric(runif.tri(1,Tr)$g)  #try also M<-c(1.6,1.2)

S<-rbind(Xp[1,],Xp[2,])
Idom.setAStri(S,Xp,Tr,M)

S<-rbind(Xp[1,],Xp[2,],Xp[3,],Xp[5,])
Idom.setAStri(S,Xp,Tr,M)

S<-rbind(c(.1,.1),c(.3,.4),c(.5,.3))
Idom.setAStri(S,Xp,Tr,M)

Idom.setAStri(c(.2,.5),Xp,Tr,M)
Idom.setAStri(c(.2,.5),c(.2,.5),Tr,M)
Idom.setAStri(Xp[5,],Xp[2,],Tr,M)

S<-rbind(Xp[1,],Xp[2,],Xp[3,],Xp[5,],c(.2,.5))
Idom.setAStri(S,Xp[3,],Tr,M)

Idom.setAStri(Xp,Xp,Tr,M)

P<-c(.4,.2)
S<-Xp[c(1,3,4),]
Idom.setAStri(Xp,P,Tr,M)
Idom.setAStri(S,P,Tr,M)
Idom.setAStri(S,Xp,Tr,M)

Idom.setAStri(rbind(S,S),Xp,Tr,M)