PTAS for Minimum k-Path Connected Vertex Cover in Growth-Bounded Graphs

In the paper, we present a polynomial-time approximation scheme (PTAS) for the minimum k-path connected vertex cover (MkPCVC) problem, which can be used to solve security problems in wireless sensor networks (WSNs), under fixed k >= 2. In contrast to previously known approximation schemes for MkPCVC problem, our approach does not need location data of the vertices, and it can be applied to growth-bounded graphs. For any epsilon(1)>0, the algorithm returns a (1+ epsilon(1))-approximation MkPCVC. We have proved the correctness and performance of the algorithm and shown its runtime is rn(O(f(r))), where f(r) is a polynomial function, r = O((1/epsilon).ln(1/epsilon)) and e is only dependent on k and epsilon(1).