Abstract
In network communication systems, frequently messages are routed along a minimum diameter spanning tree (MDST) of the network, to minimize the maximum delay in delivering a message. When a transient edge failure occurs, it is important to choose a temporary replacement edge which minimizes the diameter of the new spanning tree. Such an optimal replacement is called the best swap. As a natural extension, the all-best-swaps (ABS) problemis the problem of finding the best swap for every edge of the MDST. Given a weighted graph G = (V,E), where |V| = n and |E| = m, we solve the ABS problem in \( O\left( {n\sqrt m } \right) \) time and O(m + n) space, thus improving previous bounds for m = o(n 2).
On leave to Computer Science Dept., Carnegie Mellon University, 15213 Pittsburgh, PA, supported by the CNR under the fellowship N.215.29
The work of this author was partially supported by grant “Combinatorics and Geometr” of the Swiss National Science Foundation.
This research was carried out while the first two authors visited the third author within the CHOROCHRONOS TMR program of the European Community.
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
S. Alstrup, J. Holm, K. de Lichtenberg and M. Thorup, Minimizing diameters of dynamic trees, Proc. 24th Int. Coll. on Automata, Languages and Programming (ICALP), (1997) 270–280.
D. Eppstein, Z. Galil and G.F. Italiano, Dynamic graph algorithms, Tech. Rep. CS96-11, Univ. Ca’ Foscari di Venezia (1996).
G.N. Frederickson, Data structures for on-line updating of minimum spanning trees, SIAM J. Computing, 14 (1985) 781–798.
G.N. Frederickson, Ambivalent data structures for dynamic 2-edge connectivity and k smallest spanning trees. Proc. 32nd IEEE Symp. on Foundations of Computer Science (FOCS), (1991) 632–641.
M. Grötschel, C.L. Monma and M. Stoer, Design of survivable networks, in: Handbooks in OR and MS, Vol. 7, Elsevier (1995) 617–672.
F. Harary, Graph Theory, Addison-Wesley, Reading, MA, 1969.
G.F. Italiano and R. Ramaswami, Maintaining spanning trees of small diameter, Proc. 21st Int. Coll. on Automata, Languages and Programming (ICALP), (1994) 212–223. A revised version will appear in Algorithmica.
K. Iwano and N. Katoh, Efficient algorithms for finding the most vital edge of a minimum spanning tree, Info. Proc. Letters, 48 (1993) 211–213.
K. Malik, A.K. Mittal and S.K. Gupta, The k most vital arcs in the shortest path problem, Oper. Res. Letters, 8 (1989) 223–227.
E. Nardelli, G. Proietti and P. Widmayer, Finding the detour-critical edge of a shortest path between two nodes, Info. Proc. Letters, to appear.
R.E. Tarjan and J. van Leeuwen, Worst-case analysis of set union algorithms, JACM, 31(2) (1984) 245–281.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1998 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Nardelli, E., Proietti, G., Widmayer, P. (1998). Finding All the Best Swaps of a Minimum Diameter Spanning Tree Under Transient Edge Failures. In: Bilardi, G., Italiano, G.F., Pietracaprina, A., Pucci, G. (eds) Algorithms — ESA’ 98. ESA 1998. Lecture Notes in Computer Science, vol 1461. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-68530-8_5
Download citation
DOI: https://doi.org/10.1007/3-540-68530-8_5
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-64848-2
Online ISBN: 978-3-540-68530-2
eBook Packages: Springer Book Archive