Augmenting Trees to Meet Biconnectivity and Diameter Constraints

  title={Augmenting Trees to Meet Biconnectivity and Diameter Constraints},
  author={Victor Chepoi and Yann Vax{\`e}s},
Given a graph G=(V,E) and a positive integer D , we consider the problem of finding a minimum number of new edges E' such that the augmented graph G'=(V,E\cup E') is biconnected and has diameter no greater than D. In this note we show that this problem is NP-hard for all fixed D , by employing a reduction from the DOMINATING SET problem. We prove that the problem remains NP-hard even for forests and trees, but in this case we present approximation algorithms with worst-case bounds 3 (for even D… CONTINUE READING
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