Abstract
In a network, the distsum of a path is the sum of the distances of all vertices to the path, and the eccentricity is the maximum distance of any vertex to the path. The Cent-dian problem is the constrained optimization problem which seeks to locate on a network a path which has minimalv alue of the distsum over all paths whose eccentricity is bounded by a fixed constant. We consider this problem for trees, and we also consider the problem where an additional constraint is required, namely that the optimal path has length bounded by a fixed constant. The first problem has already been considered in the literature. We give another linear time algorithm for this problem which is considerably simpler than the previous one. The second problem does not seem to have been considered elsewhere, and we give an O(n log2 n) divide-and-conquer algorithm for its solution.
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
I. Averbakh and O. Berman.: Algorithms for path medi-center of a tree. Computers and Operations Research, 26 (1999) 1395–1409.
R. I. Becker.: Inductive algorithms on finite trees. Quaestiones Mathematicae, 13 (1990) 165–181.
R. I. Becker, Y. Chiang, I. Lari, A. Scozzari, and G. Storchi.: Finding the ℓ-core of a tree. Quaderni del Di partimento di Statistica, Probabilitá e Statistiche Applicate, 15 (1999). To appear, Discrete Applied Mathematics.
A. J. Goldman.: Optimum center location in simple networks. Transportation Science, 5 (1971) 212–221.
J. Halpern.: The location of a center-median convex combination on an undirected tree. Journalof RegionalS cience, 16 (1976) 237–245.
J. Halpern.: Finding minimal center-median convex combination (cent-dian) of a graph. Management Science, 24 (1978) 534–544.
O. Kariv and S. L. Hakimi.: An algorithmic approach to network location problems. ii: The p-medians. SIAM journalof Applied Mathematics, 37 (1979) 539–560.
T. U. Kim, T. J. Lowe, A. Tamir, and J. E. Ward.: On the location of a tree-shaped facility. Networks, 28 (1996) 167–175.
M. Labbé, D. Peeters, and J. F. Thisse.: Location on networks. Handbooks in O. R. and M. S., 8 (1995) 551–624.
C. A. Morgan and J. P. Slater.: A linear algorithm for a core of a tree. Journal of Algorithms, 1 (1980) 247–258.
S. Peng and W. Lo.: Efficient algorithms for finding a core of a tree with a specified length. Journal of Algorithms, 20 (1996) 445–458.
P. J. Slater.: Locating central paths in a network. Transportation Science, 16 (1982) 1–18.
A. Tamir.: An O(pn 2) algorithm for the p-median and related problems on tree graphs. Operation Research Letters, 19 (1996) 59–64.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Becker, R.I., Chiang, YI., Lari, I., Scozzari, A. (2001). The Cent-dian Path Problem on Tree Networks. In: Eades, P., Takaoka, T. (eds) Algorithms and Computation. ISAAC 2001. Lecture Notes in Computer Science, vol 2223. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45678-3_63
Download citation
DOI: https://doi.org/10.1007/3-540-45678-3_63
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-42985-2
Online ISBN: 978-3-540-45678-0
eBook Packages: Springer Book Archive