Minimizing Diameters of Dynamic Trees

  title={Minimizing Diameters of Dynamic Trees},
  author={Stephen Alstrup and Jacob Holm and K. D. Lichtenberg and M. Thorup},
In this paper we consider an on-line problem related to minimizing the diameter of a dynamic tree T. A new edge f is added, and our task is to delete the edge e of the induced cycle so as to minimize the diameter of the resulting tree TU {f}{e}. Starting with a tree with n nodes, we show how each such best swap can be found in worst-case O(log2n) time. The problem was raised by Italiano and Ramaswami at ICALP'94 together with a related problem for edge deletions. Italiano and Ramaswami solved… Expand
59 Citations
Dynamic Trees
  • PDF
Dynamic Subtrees Queries Revisited: The Depth First Tour Tree
  • 1
  • PDF
Finding All the Best Swaps of a Minimum Diameter Spanning Tree under Transient Edge Failures
  • 20
  • PDF
Efficient fully dynamic elimination forests with applications to detecting long paths and cycles
  • Highly Influenced
Dynamic Graph Algorithms Using Dynamic Forest Techniques
  • Lawrence Wu llwu
  • 2014
  • Highly Influenced
  • PDF
Self-adjusting top trees
  • 51
  • PDF
Sublinear-Time Maintenance of Breadth-First Spanning Trees in Partially Dynamic Networks
  • 6
  • PDF
The Tree Inclusion Problem: In Optimal Space and Faster
  • 24
  • PDF


Maintaining Spanning Trees of Small Diameter
  • 24
A Simple Parallel Algorithm for Computing the Diameters of all Vertices in a Tree and its Application
  • Z. Chen
  • Mathematics, Computer Science
  • Inf. Process. Lett.
  • 1992
  • 5
Data Structures for On-Line Updating of Minimum Spanning Trees, with Applications
  • 377
Ambivalent Data Structures for Dynamic 2-Edge-Connectivity and k Smallest Spanning Trees
  • 138
Multiwavelength lightwave networks for computer communication
  • R. Ramaswami
  • Computer Science
  • IEEE Communications Magazine
  • 1993
  • 346
Mantaining spanning trees of small diameter. Unpublished revised version of the ICALP paper
  • Mantaining spanning trees of small diameter. Unpublished revised version of the ICALP paper
  • 1996
Multi-wavelength lightwave networks for computer communi- cation
  • IEEE Communications Magazine,
  • 1993
Minimax location of a facility in an undirected tree network
  • Transportation. Sci
  • 1973