Covering a laminar family by leaf to leaf links Original Research Article

The Tree Augmentation Problem (TAP) is: given a tree image and a set image of edges (called links) on image disjoint to image, find a minimum-size edge-subset image such that image is image-edge-connected. TAP is equivalent to the problem of finding a minimum-size edge-cover image of a laminar set-family. We consider the restriction, denoted LL–TAP, of TAP to instances when every link in image connects two leaves of image. The best approximation ratio for TAP is image, obtained by Even et al. (2001, 2009, 2008) , and no better ratio was known for LL–TAP. All the previous approximation algorithms that achieve a ratio better than image for TAP, or even for LL–TAP, have been quite involved.