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Two Results on Slime Mold Computations

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Becker,  Ruben
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

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Karrenbauer,  Andreas
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

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Kolev,  Pavel
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

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Mehlhorn,  Kurt
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

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Citation

Becker, R., Bonifaci, V., Karrenbauer, A., Kolev, P., & Mehlhorn, K. (2019). Two Results on Slime Mold Computations. Theoretical Computer Science, 773, 79-106. doi:10.1016/j.tcs.2018.08.027.

Cite as: http://hdl.handle.net/21.11116/0000-0002-A3AE-2
Abstract
In this paper, we present two results on slime mold computations. The first one treats a biologically-grounded model, originally proposed by biologists analyzing the behavior of the slime mold Physarum polycephalum. This primitive organism was empirically shown by Nakagaki et al. to solve shortest path problems in wet-lab experiments (Nature'00). We show that the proposed simple mathematical model actually generalizes to a much wider class of problems, namely undirected linear programs with a non-negative cost vector. For our second result, we consider the discretization of a biologically-inspired model. This model is a directed variant of the biologically-grounded one and was never claimed to describe the behavior of a biological system. Straszak and Vishnoi showed that it can $\epsilon$-approximately solve flow problems (SODA'16) and even general linear programs with positive cost vector (ITCS'16) within a finite number of steps. We give a refined convergence analysis that improves the dependence on $\epsilon$ from polynomial to logarithmic and simultaneously allows to choose a step size that is independent of $\epsilon$. Furthermore, we show that the dynamics can be initialized with a more general set of (infeasible) starting points.