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Fully Dynamic Minimum Spanning Trees

2000; Holm, de Lichtenberg, Thorup

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Encyclopedia of Algorithms

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Keywords and Synonyms

Dynamic minimum spanning forests

Problem Definition

Let \( G=(V,E) \) be an undirected weighted graph. The problem considered here is concerned with maintaining efficiently information about a minimum spanning tree of G (or minimum spanning forest if G is not connected), when G is subject to dynamic changes, such as edge insertions, edge deletions and edge weight updates. One expects from the dynamic algorithm to perform update operations faster than recomputing the entire minimum spanning tree from scratch.

Throughout, an algorithm is said to be fully dynamic if it can handle both edge insertions and edge deletions. A partially dynamic algorithm can handle either edge insertions or edge deletions, but not both: it is incremental if it supports insertions only, and decremental if it supports deletions only.

Key Results

The dynamic minimum spanning forest algorithm presented in this section builds upon the dynamic connectivity algorithm described in the entry...

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Recommended Reading

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Author information

Authors and Affiliations

  1. Department of Information and Computer Systems, University of Rome, Rome, Italy

    Giuseppe F. Italiano

Authors
  1. Giuseppe F. Italiano
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Editor information

Editors and Affiliations

  1. Department of Electrical Engineering and Computer ScienceMcCormick School of Engineering and Applied Science, Northwestern University, Evanston, IL, 60208, USA

    Ming-Yang Kao Professor of Computer Science

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© 2008 Springer-Verlag

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Italiano, G. (2008). Fully Dynamic Minimum Spanning Trees. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-30162-4_156

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