1d:T7de,# The domination number of Proportional Edge Proximity Catch Digraph (PE-PCD) for 1D data 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`. `Yp` determines the end points of the intervals (i.e., partition the real line via intervalization). It also includes the domination numbers in the end-intervals, with interval label 1 for the left end-interval and $|Yp|+1$ for the right end-interval. If there are duplicates of `Yp` points, only one point is retained for each duplicate value, and a warning message is printed. PE proximity region is constructed with expansion parameter $r \ge 1$ and centrality parameter $c \in (0,1)$. ```r PEdom.num1D(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`). ## Returns A `list` with three 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 the PE-PCD. - **ind.mds**: The data indices of the minimum dominating set of the PE-PCD whose vertices are `Xp` points. - **int.dom.nums**: Domination numbers of the PE-PCD components for the partition intervals. ## Examples ```r a<-0; b<-10 c<-.4 r<-2 #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.num1D(Xp,Yp,r,c) PEdom.num1D(Xp,Yp,r,c=.25) PEdom.num1D(Xp,Yp,r=1.25,c) ``` ## See Also `PEdom.num.nondeg` ## Author(s) Elvan Ceyhan

PEdom.num1D function