itnews.com.au: Supercolony trails follow mathematical Steiner tree.

Via: slashdot.org: Ants Build Cheapest Networks

“We found that ants almost always made networks that minimised the total amount of trail, consistent with optimisation at a colony level, rather than at an individual level,” Latty told iTnews. “In many cases, they did a remarkable job of making networks that looked almost exactly like the mathematical shortest path, called a ‘Steiner tree’.”

wikipedia.org: Steiner tree problem

The Steiner tree problem is superficially similar to the minimum spanning tree problem: given a set V of points (vertices), interconnect them by a network (graph) of shortest length, where the length is the sum of the lengths of all edges. The difference between the Steiner tree problem and the minimum spanning tree problem is that, in the Steiner tree problem, extra intermediate vertices and edges may be added to the graph in order to reduce the length of the spanning tree.