Chapter 3: Optimal Trees and Branchings - UKP
Chapter 3: Optimal Trees and Branchings - UKP
Chapter 3: Optimal Trees and Branchings - UKP
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<strong>Optimal</strong> <strong>Trees</strong> <strong>and</strong> <strong>Branchings</strong><br />
Implementation of Kruskal’s Algorithm (2)<br />
We would like to make use of a data structure that supports the following<br />
operations efficiently:<br />
Given a set of nodes V of fixed size, <strong>and</strong> an edge set T that increases<br />
stepwise: in every step, an edge is inserted into T . At no time, an edge is<br />
removed from T .<br />
During the rise of T , we would like to know the connected components in<br />
every iteration. That is, for every node v ∈ V , we would like to compute its<br />
connected component efficiently.<br />
If we identify u <strong>and</strong> v to be part of two separate connected components, we<br />
would like to merge these components efficiently by insertion of an edge<br />
e = (v, w).<br />
Efficient Graph Algorithms | Wolfgang Stille | WS 2011/2012 | <strong>Chapter</strong> III - <strong>Optimal</strong> <strong>Trees</strong> <strong>and</strong> <strong>Branchings</strong> | 27
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