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.
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A branch-and-bound algorithm with custom node selection, branching rules, and conflict definitions solves the logic-constrained shortest path problem for flight planning with traffic flow restrictions, showing order-of-magnitude speedups on a public global dataset with 20000 real constraints.
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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.
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Logic-Constrained Shortest Paths for Flight Planning
A branch-and-bound algorithm with custom node selection, branching rules, and conflict definitions solves the logic-constrained shortest path problem for flight planning with traffic flow restrictions, showing order-of-magnitude speedups on a public global dataset with 20000 real constraints.