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Page 2 Lecture Notes in Computer Science 2865 Edited by G. Goos ...

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Topology Control Problems 197<strong>by</strong> the approximation algorithm. For space reasons, the proofs of the lemmasare omitted.Lemma 4. For the graph G 1 constructed <strong>in</strong> Step 2 of the algorithm, the weightof a m<strong>in</strong>imum connected dom<strong>in</strong>at<strong>in</strong>g set is at most OPT(I).⊓⊔Lemma 5. Consider the dom<strong>in</strong>at<strong>in</strong>g set D 1 found <strong>in</strong> Step 3 of the algorithm(Figure 2).(a) Let W (D 1 ) denote the total weight of the nodes <strong>in</strong> D 1 . Then, W (D 1 )

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