We give simple and easy-to-analyze randomized approximation algorithms
for several well-studied NP-hard network design problems.  Our
algorithms improve over the previously best known approximation ratios.  
Our main results are the following.

- We give a randomized 3.55-approximation algorithm for the connected 
  facility location problem.  The algorithm requires three lines to 
  state, one page to analyze, and improves the best-known performance 
  guarantee for the problem.

- We give a 5.55-approximation algorithm for virtual private network 
  design.  Previously, constant-factor approximation algorithms were 
  known only for special cases of this problem.

- We give a simple constant-factor approximation algorithm for the
  single-sink buy-at-bulk network design} problem.  Our performance 
  guarantee improves over what was previously known, and is an order 
  of magnitude improvement over previous combinatorial approximation 
  algorithms for the problem.