PAFP is FPT by BFS-width plus backward arcs in the union digraph and polynomial-time solvable via 2-SAT for DAGs of exact-length width 2, with matching NP-hardness for width 3.
Discrete Applied Mathematics161(10–11), 1506–1512 (2013)
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Layer-Based Width for PAFP
PAFP is FPT by BFS-width plus backward arcs in the union digraph and polynomial-time solvable via 2-SAT for DAGs of exact-length width 2, with matching NP-hardness for width 3.