slime mold Physarum polycephalum has demonstrated its ability to solve shortest

path problems and to design efficient networks, see Figure \\ref{Wet-Lab

Experiments} for illustrations. Physarum polycephalum is a slime mold in the

Mycetozoa group. For the shortest path problem, a mathematical model for the

evolution of the slime was proposed in \\cite{Tero-Kobayashi-Nakagaki} and its

biological relevance was argued. The model was shown to solve shortest path

problems, first in computer simulations and then by mathematical proof. It was

later shown that the slime mold dynamics can solve more general linear programs

and that many variants of the dynamics have similar convergence behavior. In

this paper, we introduce a dynamics for the network design problem. We

formulate network design as the problem of constructing a network that

efficiently supports a multi-commodity flow problem. We investigate the

dynamics in computer simulations and analytically. The simulations show that

the dynamics is able to construct efficient and elegant networks. In the

theoretical part we show that the dynamics minimizes an objective combining the

cost of the network and the cost of routing the demands through the network. We

also give alternative characterization of the optimum solution.

},\n}\n'