Abstract
In recent years a large number I/O-efficient 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, breadth-first search and topological sorting problems 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 previous algorithms are all considerably more complicated than our algorithms and use Θ(sort(N)) I/Os even if a partition is known. Unlike the previous algorithm, our topological sorting algorithm is simple enough to be of practical interest.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
NASA Earth Observing System (EOS) project , http://eos.nasa.gov/
Aggarwal, A., Vitter, J.S.: The Input/Output complexity of sorting and related problems. Communications of the ACM 31(9), 1116–1127 (1988)
Arge, L., Brodal, G.S., Toma, L.: On external memory MST, SSSP and multiway planar graph separation. In: Halldórsson, M.M. (ed.) SWAT 2000. LNCS, vol. 1851, pp. 433–447. Springer, Heidelberg (2000)
Arge, L., Meyer, U., Toma, L., Zeh, N.: On external-memory planar depth first search. Journal of Graph Algorithms 7(2), 105–129 (2003)
Arge, L., Toma, L., Vitter, J.S.: I/O-efficient algorithms for problems on gridbased terrains. ACM Journal on Experimental Algorithmics 6(1) (2001)
Arge, L., Toma, L., Zeh, N.: I/O-efficient topological sorting of planar DAGs. In: Proc. ACM Symposium on Parallel Algorithms and Architectures, pp. 85–93 (2003)
Arge, L., Zeh, N.: I/O-efficient strong connectivity and depth-first search for directed planar graphs. In: Proc. IEEE Symposium on Foundations of Computer Science, pp. 261–270 (2003)
Buchsbaum, L., Goldwasser, M., Venkatasubramanian, S., Westbrook, J.R.: On external memory graph traversal. In: Proc. ACM-SIAM Symposium on Discrete Algorithms, pp. 859–860 (2000)
Chiang, Y.-J., Goodrich, M.T., Grove, E.F., Tamassia, R., Vengroff, D.E., Vitter, J.S.: External-memory graph algorithms. In: Proc. ACM-SIAM Symposium on Discrete Algorithms, pp. 139–149 (1995)
Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to Algorithms, 2nd edn. The MIT Press, Cambridge
Frederickson, G.N.: Fast algorithms for shortest paths in planar graphs, with applications. SIAM Journal on Computing 16, 1004–1022 (1987)
Kumar, V., Schwabe, E.: Improved algorithms and data structures for solving graph problems in external memory. In: Proc. IEEE Symp. on Parallel and Distributed Processing, pp. 169–177 (1996)
Lipton, R.J., Tarjan, R.E.: A separator theorem for planar graphs. SIAM Journal of Applied Math 36, 177–189 (1979)
Maheshwari, A., Zeh, N.: I/O-optimal algorithms for planar graphs using separators. In: Proc. ACM-SIAM Symposium on Discrete Algorithms, pp. 372–381 (2002)
Meyer, U., Sanders, P., Sibeyn, J.F. (eds.): Algorithms for Memory Hierarchies. LNCS, vol. 2625. Springer, Heidelberg (2003)
NASA Jet Propulsion Laboratory.: NASA Shuttle Radar Topography Mission (SRTM) , http://www.jpl.nasa.gov/srtm/
Toma, L.: External Memory Graph Algorithms and Applications to Geographic Information Systems. PhD thesis, Duke University (2003)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Arge, L., Toma, L. (2004). Simplified External Memory Algorithms for Planar DAGs. In: Hagerup, T., Katajainen, J. (eds) Algorithm Theory - SWAT 2004. SWAT 2004. Lecture Notes in Computer Science, vol 3111. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-27810-8_42
Download citation
DOI: https://doi.org/10.1007/978-3-540-27810-8_42
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-22339-9
Online ISBN: 978-3-540-27810-8
eBook Packages: Springer Book Archive