It is an abstract representation of the problem faced by states and municipalities when they plan their road network.
Johnson, Lenstra and Kan prove that the problem is NP-hard, even for the simple case where all edge weights are equal and the budget restricts the choice to spanning trees.
[3] Boffey and Hinxman present a heuristic method, and show that it yields high quality results.
They also study solution methods based on branch-and-Bound, and evaluate the effects of making various approximations when calculating lower bounds.
They also generalize the problem to networks with link construction cost not proportional to length, and with trip demands that are not all equal.