Hfrhyu

I need to draw something like this (forgive me, it is very crude), to denote the dependencies in my algorithm.
Basically, I want to say that the circle (l,r) has incoming arrows from the 3 other circles (l,r-1), (l-1,r-1) and (l-1,r).
I could only come up with a grid, using Tikz. how does one draw the dependency arrows and nodes as in the below image?

documentclass[24point]article
usepackagetikz

begindocument

begintikzpicture
draw[step=0.5cm,color=gray] (-1,-1) grid (1,1);
foreach x/y/m in +0.75/+0.75/,-0.75/-0.75/ % etc
 node at (x,y) m;
endtikzpicture%

enddocument

I would draw your diagram like this

documentclass[tikz]standalone
begindocument
begintikzpicture[>=stealth]
foreach i in 0,1,2,3.5,4.5,5.5,7,8 
 draw[gray,very thin] (0,i) -- (8.5,i);
 draw[gray,very thin] (i,0) -- (i,8.5);

draw[<->] (8.5,0) node[below] $n$ -- (0,0) node[below left] $(1,1)$ -- (0,8.5) node[left] $n$;
draw[->] (2,-.5) -- (3,-.5) node[above,near start] $r$;
foreach i in 2.75,6.25 
 foreach j in .5,1.5,4,5,7.5 
 node at (i,j) $cdots$;
 node at (j,i) $vdots$;
 
 foreach j in 2.75,6.25
 node at (i,j) reflectbox$ddots$;

beginscope[every node/.style=
 circle,draw,
 minimum size=.8cm,
 align=center,
 font=footnotesize,
 inner sep=0pt
]
 node at (4,4) (11) $scriptstyle l-1$\[-1ex]$scriptstyle r-1$;
 node at (5,4) (21) $scriptstyle l-1$\[-1ex]$scriptstyle r$;
 node at (4,5) (12) $scriptstyle l$\[-1ex]$scriptstyle r-1$;
 node at (5,5) (22) $scriptstyle l$\[-1ex]$scriptstyle r$;
endscope
draw[thick,red,->] (11) -- (22);
draw[thick,red,->] (12) to[bend left=45] (22);
draw[thick,red,->] (21) to[bend right=45] (22);
endtikzpicture
enddocument

Using a loop here is probably over-killing, but anyway, here is a modification of your code. Single draw command to do this ;)

documentclass[tikz,border=7pt]standalone
begindocument
 tikz
 draw[nodes=inner sep=1pt,color=gray]
 (0,0) grid[shift=(-.5,-.5)] (4,4)
 foreach[count=i] x/y/m in 2/3/a,2/2/b,3/3/c,(x,y) node(ni) m
 (n1) edge[red,-latex] (n3)
 (n2) edge[red,-latex] (n3)
 ;
enddocument