Lecture 5 : Physarum Computations

By Prof. Kurt Mehlhorn, 2012




Physarum is a slime mold. It was observed over the past 10 years that the mold is able to solve shortest path problems and to construct good Steiner networks (Nakagaki-Yamada-Toth,Tero-Takagi-etal). In a nutshell, the shortest path experiment is as follows: A maze is built and the mold is made to cover the entire maze. Food is then provided at two positions and and the evolution of the slime is observed. Over time, the slime retracts to the shortest path connecting the two food sources.

A video showing the wet-lab experiment can be found here.

A mathematical model of the slime's dynamic behavior was proposed in 2007 by Tero-Kobayashi-Nakagaki. Extensive computer simulations of the mathematical model confirm the experimental findings. For the edges on the shortest path, the diameter converges to a fixed value, and for the edges off the shortest path, the diameter converges to zero.

We review the wet-lab and computer experiments and provide a proof for these experimental findings. We also suggest avenues for further work.

The talk is based on joint work with Vincenzo Bonifaci (Rome) and Girish Varma (TIFR).

Biodata of the Speaker:

Kurt Melhorn is a Director of the MPI for Informatics and Professor of Computer Science at the Saarland University. He heads the algorithms and complexity group at the MPI.

Kurt is one of the leading proponents of making algorithms useful. He co-created the LEDA software library containing optimized implementations of a number of algorithms. The library is widely used all over the world. He has co-authored around 200 papers and has graduated around 50 students.

Kurt has received several awards and honors including Honorary Doctorates from Magdeburg, Waterloo and Aarhus universities, the Leibniz award, the KArl Heinz Beckurts award, the Konrad Zuse medal, the EATCS award and the ACM Paris Kanellakis Theory and Practice award. He is an ACM fellow, a member of the German Academy of Sciences and the German Academy of Science and Engineering. From 2002 till 2008 he was the Vice President of the Max Planck Society.