  Lattice paths are functional entities that model efficient navigation in
discrete/grid maps. This paper presents a new scheme to generate collision-free
lattice paths with utmost efficiency using the bijective property to rooted
ordered trees, rendering a one-dimensional search problem. Our computational
studies using ten state-of-the-art and relevant nature-inspired swarm
heuristics in navigation scenarios with obstacles with convex and non-convex
geometry show the practical feasibility and efficiency in rendering
collision-free lattice paths. We believe our scheme may find use in devising
fast algorithms for planning and combinatorial optimization in discrete maps.
