PEdom.num1Dnondeg | R Documentation |
Returns the domination number, a minimum dominating set of PE-PCD whose vertices are the 1D data set Xp
,
and the domination numbers for partition intervals based on Yp
when PE-PCD is constructed with vertex regions based on non-degeneracy centers.
Yp
determines the end points of the intervals
(i.e., partition the real line via intervalization).
PE proximity regions are defined with respect to the intervals based on Yp
points with
expansion parameter r \ge 1
and
vertex regions in each interval are based on the centrality parameter c
which is one of the 2 values of c
(i.e., c \in \{(r-1)/r,1/r\}
)
that renders the asymptotic distribution of domination number
to be non-degenerate for a given value of r
in (1,2)
and c
is center of mass for r=2
.
These values are called non-degeneracy centrality parameters
and the corresponding centers are called
nondegeneracy centers.
PEdom.num1Dnondeg(Xp, Yp, r)
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 in |
A list
with three elements
dom.num |
Domination number of PE-PCD with vertex set |
mds |
A minimum dominating set of the PE-PCD. |
ind.mds |
The data indices of the minimum dominating set of the PE-PCD
whose vertices are |
int.dom.nums |
Domination numbers of the PE-PCD components for the partition intervals. |
Elvan Ceyhan
PEdom.num.nondeg
## Not run:
a<-0; b<-10
r<-1.5
#nx is number of X points (target) and ny is number of Y points (nontarget)
nx<-15; 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)
PEdom.num1Dnondeg(Xp,Yp,r)
PEdom.num1Dnondeg(Xp,Yp,r=1.25)
## End(Not run)
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