PTAS for minimum connected dominating set with routing cost constraint in wireless sensor networks

Abstract

To reduce routing cost and to improve road load balance, we study a problem of minimizing size of connected dominating set D under constraint that for any two nodes u and v, the routing cost through D is within a factor of α from the minimum, the cost of the shortest path between u and v. We show that for α ≥ 5, this problem in unit disk graphs has a polynomial-time approximation scheme, that is, for any ε > 0, there is a polynomial-time (1 + ε)-approximation. © 2010 Springer-Verlag.