Abstract
We present a fast approximation algorithm for the 1-median problem. Our algorithm can be applied to metric undirected graphs with node weight. Given a node v, our algorithm repeatedly finds a better node by making use of a shortest path tree of the previous node. We empirically show that our algorithm runs much faster and has better approximation ratio than a sophisticated existing method called DTZ. We demonstrate the effectiveness of our algorithm through experiments.
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
Barabási, A., Albert, R., Jeong, H.: Mean-field theory for scale-free random networks. Physica A: Statistical Mechanics and its Applications 272(1), 173–187 (1999)
Erdős, P., Rényi, A.: On the evolution of random graphs. Akad. Kiadó (1960)
Freeman, L.: Centrality in social networks conceptual clarification. Social Networks 1(3), 215–239 (1979)
Fujiwara, Y., Onizuka, M., Kitsuregawa, M.: Efficient Centrality Monitoring for Time-Evolving Graphs. In: Huang, J.Z., Cao, L., Srivastava, J. (eds.) PAKDD 2011, Part II. LNCS, vol. 6635, pp. 38–50. Springer, Heidelberg (2011)
Hakimi, S.L.: Optimum locations of switching centers and the absolute centers and medians of a graph. Operations Research, 450–459 (1964)
Indyk, P.: Sublinear time algorithms for metric space problems. In: Proceedings of the Thirty-first Annual ACM Symposium on Theory of Computing, pp. 428–434. ACM (1999)
Jain, K., Vazirani, V.: Approximation algorithms for metric facility location and k-median problems using the primal-dual schema and lagrangian relaxation. Journal of the ACM (JACM) 48(2), 274–296 (2001)
Leskovec, J.: Stanford large network dataset collection, http://snap.stanford.edu/data/index.html (accessed: May 04, 2012)
Rattigan, M., Maier, M., Jensen, D.: Using structure indices for efficient approximation of network properties. In: Proceedings of the 12th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 357–366. ACM (2006)
Thorup, M.: Undirected single-source shortest paths with positive integer weights in linear time. Journal of the ACM (JACM) 46(3), 362–394 (1999)
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
Tabata, K., Nakamura, A., Kudo, M. (2012). Fast Approximation Algorithm for the 1-Median Problem. In: Ganascia, JG., Lenca, P., Petit, JM. (eds) Discovery Science. DS 2012. Lecture Notes in Computer Science(), vol 7569. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33492-4_15
Download citation
DOI: https://doi.org/10.1007/978-3-642-33492-4_15
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-33491-7
Online ISBN: 978-3-642-33492-4
eBook Packages: Computer ScienceComputer Science (R0)