Dual-Fitting Approximation Algorithms for Network Connectivity Problems

We consider the NP-complete network connectivity problem of Dual Power Assignment (DPA). This models an ad hoc networks where each node can either operate at high or low power. The goal is to produce a minimum power strongly connected network. We give a Dual-Fitting algorithm to DPA with a 3/2-approximation ratio, improving the previous best know approximation of 11/7 ≈ 1.57. Another standard network design problem is Minimum Strongly Connected Spanning Subgraph (MSCS). We propose a new problem generalizing MSCS and DPA called Star Strong Connectivity (SSC). Then we show that our Dual-Fitting approach achieves a 1.6approximation ratio to SSC. This Dual-Fitting approach may have applications to other connectivity programs with cut-based linear programming relaxations. As a result of our approximations, we prove new upper bounds on the integrality gaps of these problems. For completeness, we present a family of instances of MSCS (and thus SSC) with integrality gap approaching 4/3.