Nonsmooth analysis and control theory
Nonsmooth analysis and control theory
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Electrical flows, laplacian systems, and faster approximation of maximum flow in undirected graphs
Proceedings of the forty-third annual ACM symposium on Theory of computing
Collaborative search on the plane without communication
PODC '12 Proceedings of the 2012 ACM symposium on Principles of distributed computing
A slime mold solver for linear programming problems
CiE'12 Proceedings of the 8th Turing Centenary conference on Computability in Europe: how the world computes
Natural algorithms and influence systems
Communications of the ACM
Physarum can compute shortest paths: A short proof
Information Processing Letters
Memory lower bounds for randomized collaborative search and implications for biology
DISC'12 Proceedings of the 26th international conference on Distributed Computing
Physarum can compute shortest paths: convergence proofs and complexity bounds
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part II
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Physarum Polycephalum is a slime mold that apparently is 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.