Abstract
Even though a large number of I/O-efficient graph algorithms have been developed, a number of fundamental problems still remain open. For example, no space- and I/O-efficient algorithms are known for depth-first search or breadth-first search in sparse graphs. In this paper we present two new results on I/O-efficient depth-first search in an important class of sparse graphs, namely undirected embedded planar graphs. We develop a new efficient depth-first search algorithm and show how planar depth-first search in general can be reduced to planar breadth-first search. As part of the first result we develop the first I/O-efficient algorithm for finding a simple cycle separator of a biconnected planar graph. Together with other recent reducibility results, the second result provides further evidence that external memory breadth-firstsearch is among the hardest problems on planar graphs.
Supported in part by the National Science Foundation through ESS grant EIA-9870734, RI grant EIA-9972879 and CAREER grant EIA-9984099.
Supported in part by the IST Programme of the EU under contract number IST-1999-14186 (ALCOM-FT). Part of this work was done while visiting Duke University.
Supported in part by the National Science Foundation through ESS grant EIA-9870734 and CAREER grant EIA-9984099.
Supported in part by NSERC and NCE GEOIDE research grants. Part of this work was done while visiting Duke University.
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
A. Aggarwal and J. S. Vitter. The Input/Output complexity of sorting and related problems. Communications of the ACM, 31(9):1116–1127, 1988.
L. Arge. The I/O-complexity of ordered binary-decision diagram manipulation. In Proc. Int. Symp. on Algorithms and Computation, LNCS 1004, pages 82–91, 1995.
L. Arge, G. S. Brodal, and L. Toma. On external memory MST, SSSP and multi-way planar graph separation. In Proc. Scandinavian Workshop on Algorithms Theory, LNCS 1851, pages 433–447, 2000.
L. Arge, L. Toma, and J. S. Vitter. I/O-efficient algorithms for problems on grid-based terrains. In Proc. Workshop on Algorithm Engineering and Experimentation, 2000.
A. Broder, R. Kumar, F. Manghoul, P. Raghavan, S. Rajagopalan, R. Stata, A. Tomkins, and J. Wiener. Graph structure in the web: experiments and models. In Proc. WWW Conference, 2000.
A. L. Buchsbaum, M. Goldwasser, S. Venkatasubramanian, and J. R. Westbrook. On external memory graph traversal. In Proc. ACM-SIAM Symp. on Discrete Algorithms, pages 859–860, 2000.
A. L. Buchsbaum and J. R. Westbrook. Maintaining hierarchical graph views. In Proc. ACM-SIAM Symp. on Discrete Algorithms, pages 566–575, 2000.
Y.-J. Chiang, M. T. Goodrich, E. F. Grove, R. Tamassia, D. E. Vengroff, and J. S. Vitter. External-memory graph algorithms. In Proc. ACM-SIAM Symp. On Discrete Algorithms, pages 139–149, 1995.
T. Hagerup. Planar depth-first search in O (log n) parallel time. SI AM Journal on Computing, 19(4):678–704, August 1990.
D. Hutchinson, A. Maheshwari, and N. Zeh. An external-memory data structure for shortest path queries. In Proc. Annual Combinatorics and Computing Conference, LNCS 1627, pages 51–60, 1999.
J. JáJá and R. Kosaraju. Parallel algorithms for planar graph isomorphism and related problems. IEEE Transactions on Circuits and Systems, 35(3):304–311, March 1988.
V. Kumar and E. Schwabe. Improved algorithms and data structures for solving graph problems in external memory. In Proc. IEEE Symp. on Parallel and Distributed Processing, pages 169–177, 1996.
A. Maheshwari and N. Zeh. External memory algorithms for outerplanar graphs. In Proc. Int. Symp. on Algorithms and Computation, LNCS 1741, pages 307–316, 1999.
A. Maheshwari and N. Zeh. I/O-efficient algorithms for graphs of bounded treewidth. In Proc. ACM-SIAM Symp. on Discrete Algorithms, pages 89–90, 2001.
U. Meyer. External memory bfs on undirected graphs with bounded degree. In Proc. ACM-SIAM Symp. on Discrete Algorithms, pages 87–88, 2001.
G. L. Miller. Finding small simple cycle separators for 2-connected planar graphs. Journal of Computer and System Sciences, 32(3):265–279, 1986.
K. Munagala and A. Ranade. I/O-complexity of graph algorithm. In Proc. ACM-SIAM Symp. on Discrete Algorithms, pages 687–694, 1999.
J. R. Smith. Parallel algorithms for depth-first searches I. Planar graphs. SIAM Journal on Computing, 15(3):814–830, August 1986.
J. S. Vitter. External memory algorithms and data structures. In J. Abello and J. S. Vitter, editors, External Memory Algorithms and Visualization, pages 1–38. DIMACS series in Discrete Mathematics and Theoretical Computer Science, 1999.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Arge, L., Meyer, U., Toma, L., Zeh, N. (2001). On External-Memory Planar Depth First Search. In: Dehne, F., Sack, JR., Tamassia, R. (eds) Algorithms and Data Structures. WADS 2001. Lecture Notes in Computer Science, vol 2125. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44634-6_43
Download citation
DOI: https://doi.org/10.1007/3-540-44634-6_43
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-42423-9
Online ISBN: 978-3-540-44634-7
eBook Packages: Springer Book Archive