I'm working on a problem similar to topological sorting, but with an additional constraint: I want to order the nodes by assigning a positive integer index to each, and, in additional to the relative constraints the graph defines, some nodes have a predefined index assigned.That is, the input is a set of nodes $V$, a set of relative constraints each of the form $X_a < X_b; a \in V, b \in V$, and a set of absolute constraints $X_a = i, i \in \mathbb{Z}^+$.The output is a map $X$ such that $X_a \in \mathbb{Z}^+$ for each $a \in V$, and all relative and absolute constraints specified in the input are satisfied. The values $X_a$ need not be unique; it's acceptable that $X_a = X_b$ given $a \neq b$, so long as all the specified constraints are satisfied. If no such $X$ exists, the output is an error value.Not sure what to search for; does such an algorithm exist? If not, is there a good way to map this problem to a known problem? I'm working on it, too, but just wanted to see if this set off any lightbulbs for anyone in the community before I go too deep :)(In case this helps, I'm working on a solver to manage the z-indexes of my web application.)
Topological sort, but with some fixed values
algorithms;graphs