ithm is no better than linear in the number of rates and no better than logarithmic in the number of nodes in the graph. 1 B. The Charikar-Naor-Schieber Algorithm The Charikar-Naor-Schieber algorithm =-=[5]-=- is the first constant-factor approximation algorithm given for the QoS Steiner tree problem. In its first step, all rates are rounded to the closest power of two to produce the rounded up instance of