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Paper

#### Physarum Multi-Commodity Flow Dynamics

##### MPS-Authors

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##### Fulltext (public)

arXiv:2009.01498.pdf

(Preprint), 2MB

##### Supplementary Material (public)

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##### Citation

Bonifaci, V., Facca, E., Folz, F., Karrenbauer, A., Kolev, P., Mehlhorn, K., et al. (2020). Physarum Multi-Commodity Flow Dynamics. Retrieved from https://arxiv.org/abs/2009.01498.

Cite as: http://hdl.handle.net/21.11116/0000-0007-2312-D

##### Abstract

In wet-lab experiments \cite{Nakagaki-Yamada-Toth,Tero-Takagi-etal}, the
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.