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Given a graph G and two vertices s and t in it, graph reachability is the problem of checking whether there exists a path from s to t in G. We show that reachability in directed layered planar graphs can be decided in polynomial time and \(O(n^\epsilon )\) space, for any \(\epsilon > 0\). The previous best known space bound for this problem with polynomial time was approximately \(O(\sqrt{n})\) space [1].

An $$O(n^{\epsilon })$$ Space and Polynomial Time Algorithm for Reachability in Directed Layered Planar Graphs