Abstract
Shortest paths computation in graph is one of the most fundamental operation in many applications such as social network and sensor network. When a large graph is updated with small changes, it is really expensive to recompute the new shortest path via the traditional static algorithms. To address this problem, dynamic algorithm that computes the shortest-path in response to updates is in demand. In this paper, we focus on dynamic algorithms for shortest point-to-point paths computation in directed graphs with positive edge weights. We develop novel algorithms to handle the single-edge updating and the batch edge updating. We prove that our algorithms can compute the shortest paths for updated graph in time polynomial to the size of updated part of the graph. We experimentally verify that these dynamic algorithms significantly outperform their batch counterparts in response to small changes, using real-life data and synthetic data.
This paper was partially supported by NGFR 973 grant 2012CB316200 and NSFC grant 61003046, 6111113089. Doctoral Fund of Ministry of Education of China (No.20102302120054).
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
Bauer, R., Wagner, D.: Batch dynamic single-source shortest-path algorithms: An experimental study. Experimental Algorithms 2, 1–20 (2009)
Ramalingam, G., Reps, T.: On the computational complexity of dynamic graph problems. Theoretical Computer Science 158(1-2), 233–277 (1996)
Even, S., Gazit, H.: Updating distances in dynamic graphs. J. Algorithms (1985)
Rohnert, H.: A dynamization of the all-pairs least cost problem. In: Mehlhorn, K. (ed.) STACS 1985. LNCS, vol. 182, pp. 279–286. Springer, Heidelberg (1984)
Ramalingam, G.: An incremental algorithm for a generalization of the shortest-path problem. J. Algorithms (1991)
Franciosa, P.G., Frigioni, D., Giaccio, R., Sapienza, L.: Semi-Dynamic Shortest Paths and Breadth-First Search in Digraphs. Search 2(20244) (1997)
Frigioni, D., Marchetti-spaccamela, A., Nanni, U.: Fully Dynamic Algorithms for Maintaining Shortest Paths Trees 1. Journal of Algorithms (201), 251–281 (2000)
Ausiello, G., Italiano, G.F.: Incremental algorithms for minimal length paths. J. Algorithms (1991)
Henzinger, M.R.: Faster Shortest-Path Algorithms for Planar Graphs 23, 3–23 (1997)
Fakcharoenphol, J., Rao, S.: Planar graphs, negative weight edges, shortest paths, and near linear time. Foundations (2002)
Chan, E.P.F., Yang, Y.: Shortest Path Trees Computation in Dynamic Graphs. Most, 1–45
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Liu, X., Wang, H. (2012). Dynamic Graph Shortest Path Algorithm. In: Gao, H., Lim, L., Wang, W., Li, C., Chen, L. (eds) Web-Age Information Management. WAIM 2012. Lecture Notes in Computer Science, vol 7418. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32281-5_29
Download citation
DOI: https://doi.org/10.1007/978-3-642-32281-5_29
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-32280-8
Online ISBN: 978-3-642-32281-5
eBook Packages: Computer ScienceComputer Science (R0)