 
Summary: Simplified External Memory Algorithms for
Planar DAGs
Lars Arge 1,# and Laura Toma 2
1 Duke University, Durham, NC 27708, USA, Email: large@cs.duke.edu
2 Bowdoin College, Brunswick, ME 04011, USA, Email: ltoma@bowdoin.edu
Abstract. In recent years a large number I/Oe#cient algorithms have
been developed for fundamental planar graph problems. Most of these
algorithms rely on the existence of small planar separators as well as an
O(sort(N)) I/O algorithm for computing a partition of a planar graph
based on such separators, where O(sort(N)) is the number of I/Os needed
to sort N elements.
In this paper we simplify and unify several of the known planar graph
results by developing linear I/O algorithms for the fundamental single
source shortest path, breadthfirst search and topological sorting prob
lems on planar directed acyclic graphs, provided that a partition is given;
thus our results give O(sort(N)) I/Os algorithms for the three problems.
While algorithms for all these problems were already known, the previ
ous algorithms are all considerably more complicated than our algorithms
and use #(sort(N)) I/Os even if a partition is known. Unlike the previ
ous algorithm, our topological sorting algorithm is simple enough to be
