Drawing a large graph with mathematical expressions inside vertices

Question

How do I draw a graph similar to this picture in LaTeX? The inequalities in the vertices are quite big in size, they're not small labels like A, B. I would like to have some expressions on the edges too, if it doesn't become too messy (not shown in the figure).

Note that there are 10 vertices on the left hand and over 20 on the right hand, not all of which are shown. There are multiple connections to and from nodes. So if there is an array-like way of specifying edges (e.g. draw each edge from edges = {(u1, v1), (u1, v2), (u2, v2), (u2, v3), (u3, v4)...}, then it would be better than specifying each edge manually in the figure.(e.g. draw edge (u1, v1), draw edge (u1, v2) etc.)

Also, I think I will need a bigger page size as well (I'm not going to print it, so arbitrarily large size is fine).

Preferably, I want something on the lines of: vertices list = (v1, v2, ...), edges list = ((u1, v1), (u2, v2), ...) and tikz/LaTeX to take care of the rest of the arrangement.

Answer 1

I approached the problem using TikZ and the shapes library, though I think the ellipses are not so nice for such long content. There are two chains, both going downwards (below), all nodes have a fixed height (minimum height= and ìnner ysep=) such that they are aligned by using the same stepnode distance` on both chains,

\documentclass{standalone}
\usepackage{tikz} \usetikzlibrary{chains,positioning,scopes,shapes}
\begin{document}
    \tikzstyle{myNode}=[on chain, align=center,shape=ellipse,draw, minimum width=3cm, minimum height=1cm,inner ysep=0pt]
    \begin{tikzpicture}
        \begin{scope}[start chain=going below, node distance=2cm]
            \node [on chain, myNode] (L1) at (0,-3) {\(x_1\quad x_2\)\\\(v_2\geq0\)};
            \node [on chain, myNode] (L2) {\(x_1\quad (1-x_2)\)\\\((k-1)v_2 - (k+1)v_3 \geq 0\)};   
            \node [on chain, myNode] (L3) {\(1-x_1\quad (1-x_2)\)\\\((k+1)v_1 - (2k-1)v_2 \geq 1\)};
        \end{scope}
        \begin{scope}[start chain=going below, node distance=2cm]
            \node [on chain, myNode] (K1) at (7,0) {\(x_1\quad x_2\quad x_3\)\\\(2v_2\geq0\)};
            \node [on chain, myNode] (K2) {\(x_1\quad x_2 \quad (1-x_3)\)\\\(v_2 + (k-2)v_3\geq 0 \geq 0\)};    
            \node [on chain, myNode] (K3) {\(x_1(1-x_2)(1-x_3)\)\\\((k-1)v_2 - (2k-2)v_3\geq 0\)};
            \node [on chain, myNode] (K4) {\(x_1(1-x_b)(1-x_c)\)\\\(\cdots\)};
            \end{scope}
        \draw[->] (L1) -- (K1);
        \draw[->] (L1) -- (K2);
        %
        \draw[->] (L2) -- (K2);
        \draw[->] (L2) -- (K3);
        %
        \draw[->] (L3) -- (K4);
    \end{tikzpicture}
\end{document}

Note that the first (left) chain starts exactely one height earlier (1cm height and 2cm node distance).

The result still needs some styling (and maybe other shapes than ellipse but its a starting point.

Edit/Update In the first case, all edges start at the center point, because the \draw always the start/end point to be the center. to change that one can use the meta coordinates of the nodes (.north,.east,.south and .west), i.e. using for the drawing of the edges

        \draw[->] (L1.east) -- (K1.west);
        \draw[->] (L1.east) -- (K2.west);
        %
        \draw[->] (L2.east) -- (K2.west);
        \draw[->] (L2.east) -- (K3.west);
        %
        \draw[->] (L3.east) -- (K4.west);

to obtain (includes removing the shape=ellipse and hence having rectangles):

Answer 2

Here's an approach in Metapost for comparison, using some elongated super-ellipses.

prologues := 3;
outputtemplate := "%j%c.eps";

% a little TeX alignment for each "node"
verbatimtex
\def\m#1{$\vcenter{\let\\\cr\halign{\hfil$##$\hfil\cr#1\crcr}}$}
etex

beginfig(1);

% "se" is a shape to surround each text block
path se; se = (superellipse(3 right, up, 3 left, down, 0.89)) scaled 23;

% define the source and target equations
picture source[], target[];

source1 = btex \m{x_1 x_2\\v_2\ge0} etex;
source2 = btex \m{x_1(1-x_2)\\(k-1)v_2-(k+1)v_3\ge0} etex;
source3 = btex \m{(1-x_1)(1-x_2)\\(k+1)v_1-(2k-1)v_2\ge1} etex;

target1 = btex \m{x_1 x_2 x_3\\2v_3\ge0} etex;
target2 = btex \m{x_1 x_2 (1-x_3)\\v_2+(k-2)v_3\ge0} etex;
target3 = btex \m{x_1 (1-x_2) (1-x_3)\\(k-1)v_2-(2k-2)v_3\ge0} etex;
target4 = btex \m{x_1 (1-x_b) (1-x_c)\\\dots} etex;

% u = horizontal separation, v = vertical
u = 120; v = 64;

% redefine each node with background, edge, and position; and then draw it
for i=1 upto 3:
  source[i] := image(fill se withcolor .9[blue,white]; draw se; label(source[i], origin)) shifted (-u,v*(3-i));
  draw source[i];
endfor
for i=1 upto 4:
  target[i] := image(fill se withcolor .9[red,white]; draw se; label(target[i], origin)) shifted (+u,v*(3.5-i));
  draw target[i];
endfor

% a macro to do the connnections, with neat line crossings
vardef connect(expr i,j) = 
  save A; path A;
  A = center source[i] shifted 24 right -- 
      center target[j] shifted 24 left
      cutbefore se shifted center source[i]
      cutafter  se shifted center target[j];
  undraw subpath (0.2,0.8) of A withpen pencircle scaled 3; 
  drawarrow A;
  enddef;

% one loop of each source "node"
forsuffixes $=1,2:   connect(1,$); endfor
forsuffixes $=2,3,4: connect(2,$); endfor
forsuffixes $=3,4:   connect(3,$); endfor

endfig;
end.