Designing networks with bounded pairwise distance

The problem of finding a minimum cost subset of missing links in a communication network was considered, such that adding these links to the network makes every pair of points within distance at most d from each other. A novel linear programming based approach was used to obtain an O(log n log d) approximation algorithm for the case of uniform link lengths and costs. The Ω(log n) hardness was also extended to d∈{2, 3}. On the other hand, if link costs can vary, it was shown that the problem is Ω(2^log(1-ε)n)-hard for d≥3.