Physarum Can Compute Shortest Paths: Convergence Proofs and Complexity Bounds

  • Luca Becchetti
  • Vincenzo Bonifaci
  • Michael Dirnberger
  • Andreas Karrenbauer
  • Kurt Mehlhorn
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7966)


Physarum polycephalum is a slime mold that is apparently able to solve shortest path problems. A mathematical model for the slime’s behavior in the form of a coupled system of differential equations was proposed by Tero, Kobayashi and Nakagaki [TKN07]. We prove that a discretization of the model (Euler integration) computes a (1 + ε)-approximation of the shortest path in O( m L (logn + logL)/ε 3) iterations, with arithmetic on numbers of O(log(nL/ε)) bits; here, n and m are the number of nodes and edges of the graph, respectively, and L is the largest length of an edge. We also obtain two results for a directed Physarum model proposed by Ito et al. [IJNT11]: convergence in the general, nonuniform case and convergence and complexity bounds for the discretization of the uniform case.


Short Path Equilibrium Point Short Path Problem Slime Mold Physarum Polycephalum 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Luca Becchetti
    • 1
  • Vincenzo Bonifaci
    • 2
  • Michael Dirnberger
    • 3
  • Andreas Karrenbauer
    • 3
  • Kurt Mehlhorn
    • 3
  1. 1.Dipartimento di Informatica e SistemisticaSapienza Università di RomaItaly
  2. 2.Istituto di Analisi dei Sistemi ed Informatica “Antonio Ruberti”Consiglio Nazionale delle RicercheRomeItaly
  3. 3.Max Planck Institute for InformaticsSaarbrückenGermany

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