Physarum Can Compute Shortest Paths

TL;DR

This paper proves that a mathematical model of Physarum Polycephalum's foraging behavior converges to the shortest path between two food sources, demonstrating a natural algorithm for shortest path computation.

Contribution

It provides a rigorous proof that the Physarum model converges to the shortest path, confirming experimental observations and illustrating a natural algorithm evolved by nature.

Findings

Model converges to shortest path regardless of network structure

Mathematical proof aligns with biological experiments

Demonstrates evolutionarily developed natural algorithm

Abstract

Physarum Polycephalum is a slime mold that is apparently able to solve shortest path problems. A mathematical model has been proposed by biologists to describe the feedback mechanism used by the slime mold to adapt its tubular channels while foraging two food sources s0 and s1. We prove that, under this model, the mass of the mold will eventually converge to the shortest s0 - s1 path of the network that the mold lies on, independently of the structure of the network or of the initial mass distribution. This matches the experimental observations by the biologists and can be seen as an example of a "natural algorithm", that is, an algorithm developed by evolution over millions of years.