Abstract
A core of a graph G = (V, E) is a path P in G which minimizes d(P)=∑ v∈V d(v, P) where d(v,P) is the distance of vertex v from P. Finding a core of a network is essential in locating the best sites to set up service facilities. Here we present the first distributed algorithm which finds a core of a tree network in O(D) time using O(n) messages, where D and n are the diameter and the number of vertices of G respectively.
Keywords
This research is partially supported by the Swedish Council for Engineering Sciences.
Preview
Unable to display preview. Download preview PDF.
References
Albacea, E. A.: Parallel algorithm for finding a core of a tree network. Information Processing Letters 51 (1994) 223–226
Bar-Ilan, J., Peleg, D.: Approximation algorithms for selecting network centers. Workshop on Algorithms and Data Structures (1991) 343–354
Hakim, S. L.: Optimal distribution of switching centers in a communication network and some related graph theoretical problems. Opns. Res. 13 (1965) 462–475
Korach, E.: Distributed algorithms for finding centers and medians in networks. ACM Trans. on Programming Languages and Systems 6(3) (1984) 380–401
Minieka, E., Patel, N. H.: On finding the core of a tree with a specified length. J. Algorithms 4 (1983) 345–352
Morgan, C. A., Slater, P. J.: A linear algorithm for a core of a tree. J. Algorithms. 1 (1980) 247–258
Peng, S., Lo, W.: A simple optimal parallel algorithm for a core of a tree. J. of Parallel and Distributed Computing 20 (1994) 388–392
Shier, D. R.: A min-max theorem for p-center problems on a tree. Transportation Sci. 11 (1977) 243–252
Slater, P. J.: Locating central paths in a graph. Transportation Sci. 16 (1982) 1–18
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1995 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Jennings, E. (1995). Distributed algorithm for finding a core of a tree network. In: Bartosek, M., Staudek, J., Wiedermann, J. (eds) SOFSEM '95: Theory and Practice of Informatics. SOFSEM 1995. Lecture Notes in Computer Science, vol 1012. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60609-2_22
Download citation
DOI: https://doi.org/10.1007/3-540-60609-2_22
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-60609-3
Online ISBN: 978-3-540-48463-9
eBook Packages: Springer Book Archive