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Simplified External Memory Algorithms for Planar DAGs

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


Source: Arge, Lars - Department of Computer Science, Aarhus Universitet


Collections: Computer Technologies and Information Sciences