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Two Results on Slime Mold Computations

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.

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Genre: Journal Article

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Creators:
Becker, Ruben1, Author
Bonifaci, Vincenzo2, Author
Karrenbauer, Andreas1, Author
Kolev, Pavel1, Author
Mehlhorn, Kurt1, Author
Affiliations:
1Algorithms and Complexity, MPI for Informatics, Max Planck Society, ou_24019
2External Organizations, ou_persistent22

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Free keywords: Computer Science, Data Structures and Algorithms, cs.DS,Mathematics, Dynamical Systems, math.DS,Mathematics, Optimization and Control, math.OC, Physics, Biological Physics, physics.bio-ph
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.

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Language(s): eng - English
Dates: 20182019
Publication Status: Published in print
Pages: 29 p.
Publishing info: -
Rev. Method: -
Identifiers: BibTex Citekey: BBKKM2018
DOI: 10.1016/j.tcs.2018.08.027
Degree: -

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### Source 1

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Title: Theoretical Computer Science
Source Genre: Journal
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Affiliations:
Publ. Info: Amsterdam : Elsevier
Pages: 28 p. Volume / Issue: 773 Sequence Number: - Start / End Page: 79 - 106 Identifier: ISSN: 0304-3975
CoNE: https://pure.mpg.de/cone/journals/resource/954925512450