Physarum-Inspired Multi-Commodity Flow Dynamics
Abstract
In wet-lab experiments, the slime mold Physarum polycephalum has demonstrated its ability to solve shortest path problems and to design efficient networks. For the shortest path problem, a mathematical model for the evolution of the slime is available and it has been shown in computer experiments and through mathematical analysis that the dynamics solves the shortest path problem. 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.
Keywords
Cite
@article{arxiv.2009.01498,
title = {Physarum-Inspired Multi-Commodity Flow Dynamics},
author = {Vincenzo Bonifaci and Enrico Facca and Frederic Folz and Andreas Karrenbauer and Pavel Kolev and Kurt Mehlhorn and Giovanna Morigi and Golnoosh Shahkarami and Quentin Vermande},
journal= {arXiv preprint arXiv:2009.01498},
year = {2022}
}
Comments
to appear in Theoretical Computer Science