In the network localization problem the locations of some nodes (called anchors) as well as the distances between some pairs
of nodes are known, and the goal is to determine the location of all nodes. The localization problem is said to be solvable
(or uniquely localizable) if there is a unique set of locations consistent with the given data. Recent results from graph
rigidity theory made it possible to characterize the solvability of the localization problem in two dimensions.
In this paper we address the following related optimization problem: given the set of known distances in the network, make
the localization problem solvable by designating a smallest set of anchor nodes. We develop a polynomial-time 3-approximation
algorithm for this problem by proving new structural results in graph rigidity and by using tools from matroid theory.