Abstract
In the dynamic all-pairs shortest path problem we wish to maintain information about distances in a weighted graph subject to dynamic operations such as edge insertions, edge deletions, and edge weight updates. The most efficient algorithms for this problem maintain a suitable superset of shortest paths in the graph. This superset retains information about the history of previous graph updates so as to avoid pathological situations where algorithms are continuously forced to rebuild large portions of their data structures. On the other hand, the set of maintained paths may grow too large, resulting in both prohibitive space consumption and inefficient updates. To circumvent this problem, the algorithms perform suitable path cleaning operations. In this paper, we implement and experiment with a recent efficient algorithm by Thorup, which differs from the previous algorithms mainly in the way path cleaning is done, and we carry out a thorough experimental investigation on known implementations of dynamic shortest path algorithms. Our experimental study puts the new results into perspective with respect to previous work and gives evidence that path cleaning, although crucial for the theoretical bounds, appears to be instead of very limited impact in practice.
Work supported in part by the Sixth Framework Programme of the EU under contract number 507613 (Network of Excellence EuroNGI) and under contract number 001907 (project DELIS), and by Italian MIUR under project ALGO-NEXT.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Buriol, L., Resende, M., Thorup, M.: Speeding up dynamic shortest path algorithms. Technical report, AT&T Labs Research Report TD5RJ8B (2003)
Demetrescu, C., Emiliozzi, S., Finocchi, I., Ribichini, A.: The Leonardo Library, http://www.leonardo-vm.org
Demetrescu, C., Emiliozzi, S., Italiano, G.F.: Experimental analysis of dynamic all pairs shortest path algorithms. In: Proc. 15th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2004), pp. 362–371 (2004)
Demetrescu, C., Frigioni, D., Marchetti-Spaccamela, A., Nanni, U.: Maintaining shortest paths in digraphs with arbitrary arc weights: An experimental study. In: Näher, S., Wagner, D. (eds.) WAE 2000. LNCS, vol. 1982. Springer, Heidelberg (2001)
Demetrescu, C., Italiano, G.F.: A new approach to dynamic all pairs shortest paths. J. ACM 51(6), 968–992 (2004) (preliminary version in STOC 2003)
Dijkstra, E.W.: A note on two problems in connexion with graphs. Numerische Mathematik 1, 269–271 (1959)
Fortz, B., Thorup, M.: Internet traffic engineering by optimizing OSPF weights. In: Proc. 19th IEEE INFOCOM, pp. 519–528 (2000)
Frigioni, D., Ioffreda, M., Nanni, U., Pasqualone, G.: Analysis of dynamic algorithms for the single source shortest path problem. ACM Journal on Experimental Algorithmics 3 (1998)
Frigioni, D., Miller, T., Nanni, U., Pasqualone, G., Shaefer, G., Zaroliagis, C.D.: An experimental study of dynamic algorithms for directed graphs. In: Bilardi, G., Pietracaprina, A., Italiano, G.F., Pucci, G. (eds.) ESA 1998. LNCS, vol. 1461, pp. 320–331. Springer, Heidelberg (1998)
Goldberg, A.V.: Shortest path algorithms: Engineering aspects. In: Eades, P., Takaoka, T. (eds.) ISAAC 2001. LNCS, vol. 2223. Springer, Heidelberg (2001)
Henzinger, M.R., King, V.: Maintaining minimum spanning forests in dynamic graphs. SIAM J. Computing 31(2), 364–374 (2001)
King, V.: Fully dynamic algorithms for maintaining all-pairs shortest paths and transitive closure in digraphs. In: Proc. 40th IEEE Symposium on Foundations of Computer Science (FOCS 1999), pp. 81–99 (1999)
Loubal, P.: A network evaluation procedure. Highway Research Record 205, 96–109 (1967)
Narvaez, P., Siu, K.Y., Tzeng, H.Y.: New dynamic SPT algorithm based on a ball-and-string model. IEEE/ACM Transactions on Networking 9, 706–718 (2001)
Ramalingam, G.: Bounded Incremental Computation. LNCS, vol. 1089. Springer, Heidelberg (1996)
Thorup, M.: Fully-dynamic all-pairs shortest paths: Faster and allowing negative cycles. In: Hagerup, T., Katajainen, J. (eds.) SWAT 2004. LNCS, vol. 3111, pp. 384–396. 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
Demetrescu, C., Faruolo, P., Italiano, G.F., Thorup, M. (2006). Does Path Cleaning Help in Dynamic 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_65
Download citation
DOI: https://doi.org/10.1007/11841036_65
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)