In the Group Steiner Tree problem (GST), we are given a (vertex or edge)-weighted graph $
G=(V, E) $ on $ n $ vertices, a root vertex $ r $ and a collection of groups $\{S_i\} _ {i\in [h]} …

There are growing interests in designing polynomial-time approximation schemes (PTAS)
for optimization problems in planar graphs. Many NP-hard problems are shown to admit …

This thesis explores two optimization problems, the group Steiner tree and firefighter
problems, which are known to be NP-hard even on trees. We study the approximability of …