Abstract
We present an efficient cache-oblivious implementation of the shortest-path algorithm for planar graphs by Klein et al., and prove that it incurs no more than \({\mathcal O}(\frac{N}{B^{1/2 - \epsilon}} + \frac{N}{B}{\rm log}N\)) block transfers on a graph with N vertices. This is the first cache-oblivious algorithm for this problem that incurs o(N) block transfers.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Aggarwal, A., Vitter, J.S.: The input/output complexity of sorting and related problems. Comm. ACM, 1116–1127 (1988)
Arge, L., Bender, M.A., Demaine, E., Holland-Minkley, B., Munro, J.I.: Cache-oblivious priority queue and graph algorithm applications. In: Proc. 34th STOC, pp. 268–276 (2002)
Arge, L., Brodal, G.S., Toma, L.: On external-memory MST, SSSP and multi-way planar graph separation. J. Alg. 53, 186–206 (2004)
Arge, L., Meyer, U., Toma, L.: External memory algorithms for diameter and all-pairs shortest-paths on sparse graphs. In: Díaz, J., Karhumäki, J., Lepistö, A., Sannella, D. (eds.) ICALP 2004. LNCS, vol. 3142, pp. 146–157. Springer, Heidelberg (2004)
Arge, L., Meyer, U., Toma, L., Zeh, N.: On external-memory planar depth first search. J. Graph Alg. and Appl. 7(2), 105–129 (2003)
Arge, L., Toma, L.: Simplified external memory algorithms for planar DAGs. In: Hagerup, T., Katajainen, J. (eds.) SWAT 2004. LNCS, vol. 3111, pp. 493–503. Springer, Heidelberg (2004)
Arge, L., Toma, L., Zeh, N.: I/O-efficient algorithms for planar digraphs. In: Proc. 15th SPAA, pp. 85–93 (2003)
Arge, L., Zeh, N.: I/O-efficient strong connectivity and depth-first search for directed planar graphs. In: Proc. 44th FOCS, pp. 261–270 (2003)
Brodal, G.S., Fagerberg, R.: Cache oblivious distribution sweeping. In: Widmayer, P., Triguero, F., Morales, R., Hennessy, M., Eidenbenz, S., Conejo, R. (eds.) ICALP 2002. LNCS, vol. 2380, pp. 426–438. Springer, Heidelberg (2002)
Brodal, G.S., Fagerberg, R.: Funnel heap—a cache oblivious priority queue. In: Bose, P., Morin, P. (eds.) ISAAC 2002. LNCS, vol. 2518, pp. 219–228. Springer, Heidelberg (2002)
Brodal, G.S., Fagerberg, R.: On the limits of cache-obliviousness. In: Proc. 35th STOC, pp. 307–315 (2003)
Brodal, G.S., Fagerberg, R., Meyer, U., Zeh, N.: Cache-oblivious data structures and algorithms for undirected breadth-first search and shortest paths. In: Hagerup, T., Katajainen, J. (eds.) SWAT 2004. LNCS, vol. 3111, pp. 480–492. Springer, Heidelberg (2004)
Chiang, Y.-J., Goodrich, M.T., Grove, E.F., Tamassia, R., Vengroff, D.E., Vitter, J.S.: External-memory graph algorithms. In: Proc. 6th SODA, pp. 139–149 (1995)
Chowdhury, R.A., Ramachandran, V.: Cache-oblivious shortest paths in graphs using buffer heap. In: Proc. 16th SPAA, pp. 245–254 (2004)
Dijkstra, E.W.: A note on two problems in connection with graphs. Num. Math. 1, 269–271 (1959)
Fakcharoenphol, J., Rao, S.: Planar graphs, negative weight edges, shortest paths, near linear time. In: Proc. 42nd FOCS, pp. 232–241 (2001)
Frederickson, G.N.: Fast algorithms for shortest paths in planar graphs, with applications. SIAM J. Comp. 16, 1004–1022 (1987)
Frigo, M., Leiserson, C.E., Prokop, H., Ramachandran, S.: Cache-oblivious algorithms. In: Proc. 40th FOCS, pp. 285–297 (1999)
Klein, P., Rao, S., Rauch, M., Subramanian, S.: Faster shortest path algorithms for planar graphs. J. Comp. Sys. Sci. 55, 3–23 (1997)
Maheshwari, A., Zeh, N.: I/O-optimal algorithms for planar graphs using separators. In: Proc. 13th SODA, pp. 372–381 (2002)
Pettie, S., Ramachandran, V.: Computing shortest paths with comparisons and additions. In: Proc. 13th SODA, pp. 267–276 (2002)
Thorup, M.: Undirected single source shortest paths with positive integer weights in linear time. J. ACM 46, 362–394 (1999)
Thorup, M.: Floats, integers, and single source shortest paths. J. Alg. 35, 189–201 (2000)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Jampala, H., Zeh, N. (2005). Cache-Oblivious Planar Shortest Paths. In: Caires, L., Italiano, G.F., Monteiro, L., Palamidessi, C., Yung, M. (eds) Automata, Languages and Programming. ICALP 2005. Lecture Notes in Computer Science, vol 3580. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11523468_46
Download citation
DOI: https://doi.org/10.1007/11523468_46
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-27580-0
Online ISBN: 978-3-540-31691-6
eBook Packages: Computer ScienceComputer Science (R0)