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 />
Pairwise different edge costs (cont’d)<br />
We have assumed pairwise different edge costs for all edges in E.<br />
How is it possible to conclude that the algorithms are still correct<br />
even if some edge costs are identical?<br />
Idea: modify edge costs by very small amounts δ such that all edge<br />
costs are pairwise different.<br />
The modification must be small enough in order to not change the<br />
relative ordering of edges that originally had different costs.<br />
The modification is only used as a tie-breaker for identical edge costs.<br />
If a tree T is more expensive than a tree T ′ with respect to its original<br />
costs then it is more expensive for the modified costs <strong>and</strong> vice versa.<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> | 14
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