I/O-efficient strong connectivity and depth-first search for directed planar graphs

We present the first I/O-efficient algorithms for the following fundamental problems on directed planar graphs: finding the strongly connected components, finding a simple-path 2/3-separator, and computing a depth-first spanning (DFS) tree. Our algorithms for the first two problems perform O(sort(N)) I/Os, where N = V + E and sort(N) = Θ((N/B)) is the number of I/Os required to sort N elements. The DFS-algorithm performs O(sort(N) log(N/M)) I/Os, where M is the number of elements that fit into main memory.