What is the fastest known algorithm for max flow on dags? Can there be a linear-time algorithm running in time $O(|V|+|E|)$?
Input: a weighted dag $G=(V,E,w)$ where $E$ is given as an edge list $E$ and $w$ is the edge weight function; and two vertices $s$ and $t$.
Output: a max flow from $s$ to $t$.
The dag is simple (no loops, no parallel edges). Edge weights are positive integers.