Polynomial-time approximation scheme for minimum connected dominating set under routing cost constraint in wireless sensor networks

To reduce routing cost in wireless sensor networks, we study a problem of minimizing the size of connected dominating set D under constraint that for any two nodes u and v, ^mD(u,v)≤α·m(u,v) where α is a constant, ^mD(u,v) is the number of intermediate nodes on a shortest path connecting u and v through D and m(u,v) is the number of intermediate nodes in a shortest path between u and v in a given unit disk graph. We show that for α<5, this problem has a polynomial-time approximation scheme, that is, for any ε>0, there is a polynomial-time (1+ε)- approximation.