Abstract
We present an O(n 3 (loglogn/logn)5/4) time algorithm for all pairs shortest paths. This algorithm improves on the best previous result of O(n 3/logn) time.
Research supported in part by NSF grant 0310245.
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
Aho, A.V., Hopcroft, J.E., Ullman, J.D.: The Design and Analysis of Computer Algorithms. Addison-Wesley, Reading (1974)
Aho, A.V., Hopcroft, J.E., Ullman, J.D.: Data Structures and Algorithms. Addison-Wesley, Reading (1983)
Albers, S., Hagerup, T.: Improved parallel integer sorting without concurrent writing. Information and Computation 136, 25–51 (1997)
Batcher, K.E.: Sorting networks and their applications. In: Proc. 1968 AFIPS Spring Joint Summer Computer Conference, pp. 307–314 (1968)
Chan, T.M.: All-pairs shortest paths with real weights in O(n 3/logn) time. In: Dehne, F., López-Ortiz, A., Sack, J.-R. (eds.) WADS 2005. LNCS, vol. 3608, pp. 318–324. Springer, Heidelberg (2005)
Dobosiewicz, W.: A more efficient algorithm for min-plus multiplication. Inter. J. Comput. Math. 32, 49–60 (1990)
Fredman, M.L.: New bounds on the complexity of the shortest path problem. SIAM J. Computing 5, 83–89 (1976)
Fredman, M.L., Tarjan, R.: Fibonacci heaps and their uses in improved network optimization algorithms. Journal of the ACM 34, 596–615 (1987)
Galil, Z., Margalit, O.: All pairs shortest distances for graphs with small integer length edges. Information and Computation 134, 103–139 (1997)
Han, Y.: Improved algorithms for all pairs shortest paths. Information Processing Letters 91, 245–250 (2004)
Han, Y.: Achieving O(n 3/logn) time for all pairs shortest paths by using a smaller table. In: Proc. 21st Int. Conf. on Computers and Their Applications (CATA 2006), pp. 36–37 (2006)
Pettie, S.: A faster all-pairs shortest path algorithm for real-weighted sparse graphs. In: Widmayer, P., Triguero, F., Morales, R., Hennessy, M., Eidenbenz, S., Conejo, R. (eds.) ICALP 2002. LNCS, vol. 2380, pp. 85–97. Springer, Heidelberg (2002)
Pettie, S., Ramachandran, V.: A shortest path algorithm for real-weighted undirected graphs. SIAM J. Comput. 34(6), 1398–1431 (2005)
Sankowski, P.: Shortest paths in matrix multiplication time. In: Brodal, G.S., Leonardi, S. (eds.) ESA 2005. LNCS, vol. 3669, pp. 770–778. Springer, Heidelberg (2005)
Seidel, R.: On the all-pairs-shortest-path problem in unweighted undirected graphs. J. Comput. Syst. Sci. 51, 400–403 (1995)
Takaoka, T.: A new upper bound on the complexity of the all pairs shortest path problem. Information Processing Letters 43, 195–199 (1992)
Takaoka, T.: An O(n 3 loglogn/logn) time algorithm for the all-pairs shortest path problem. Information Processing Letters 96, 155–161 (2005)
Thorup, M.: Undirected single source shortest paths with positive integer weights in linear time. Journal of ACM 46(3), 362–394 (1999)
Yuster, R., Zwick, U.: Answering distance queries in directed graphs using fast matrix multiplication. In: 46th Annual IEEE Symposium on Foundations of Computer Science, pp. 389–396. IEEE Comput. Soc., Los Alamitos (2005)
Zwick, U.: All pairs shortest paths using bridging sets and rectangular matrix multiplication. Journal of the ACM 49(3), 289–317 (2002)
Zwick, U.: A slightly improved sub-cubic algorithm for the all pairs shortest paths problem. In: Fleischer, R., Trippen, G. (eds.) ISAAC 2004. LNCS, vol. 3341, pp. 921–932. Springer, Heidelberg (2004)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Han, Y. (2006). An O(n 3 (loglogn/logn)5/4) Time Algorithm for All Pairs Shortest Paths. In: Azar, Y., Erlebach, T. (eds) Algorithms – ESA 2006. ESA 2006. Lecture Notes in Computer Science, vol 4168. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11841036_38
Download citation
DOI: https://doi.org/10.1007/11841036_38
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-38875-3
Online ISBN: 978-3-540-38876-0
eBook Packages: Computer ScienceComputer Science (R0)