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NP Completeness of Kauffman's N-k Model, A Tuneable Rugged Fitness Landscape

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  • Edward D. Weinberger

Abstract

The concept of a "fitness landscape," a picturesque term for a mapping of the vertices of a finite graph to the real numbers, has arisen in several fields, including evolutionary theory. The computational complexity of two, qualitatively similar versions of a particularly simple fitness landscape are shown to differ considerably. In one version, the question "Is the global optimum greater than a given value V?" is shown to be answerable in polynominal time by presenting an efficient algorithm that actually computes the optimum. The corresponding problem for the other version of the landscape is shown to be NP complete. The NP completeness of the latter problem leads to some speculations on why P not equal to NP. Key words. rugged fitness landscape, n-k model

Suggested Citation

  • Edward D. Weinberger, 1996. "NP Completeness of Kauffman's N-k Model, A Tuneable Rugged Fitness Landscape," Working Papers 96-02-003, Santa Fe Institute.
    • Handle: RePEc:wop:safiwp:96-02-003
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    Cited by:

    1. Ilaria Giannoccaro & Giovanni F. Massari & Giuseppe Carbone, 2018. "Team Resilience in Complex and Turbulent Environments: The Effect of Size and Density of Social Interactions," Complexity, Hindawi, vol. 2018, pages 1-11, July.
    2. Teppo Felin & Stuart Kauffman & Roger Koppl & Giuseppe Longo, 2014. "Economic Opportunity and Evolution: Beyond Landscapes and Bounded Rationality," Post-Print hal-01415115, HAL.
    3. De Vincenzo, Ilario & Massari, Giovanni F. & Giannoccaro, Ilaria & Carbone, Giuseppe & Grigolini, Paolo, 2018. "Mimicking the collective intelligence of human groups as an optimization tool for complex problems," Chaos, Solitons & Fractals, Elsevier, vol. 110(C), pages 259-266.
    4. Julian Padget & Richard Vidgen & James Mitchell & Amy Marshall & Rick Mellor, 2009. "Sendero: An Extended, Agent-Based Implementation of Kauffman's NKCS Model," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 12(4), pages 1-8.
    5. Yong-Hoon Kim & Yourim Yoon & Yong-Hyuk Kim, 2020. "Towards a Better Basis Search through a Surrogate Model-Based Epistasis Minimization for Pseudo-Boolean Optimization," Mathematics, MDPI, vol. 8(8), pages 1-17, August.
    6. Nicolás Garrido, 2004. "The Desirable Organizational Structure for Evolutionary Firms in Static Landscapes," Metroeconomica, Wiley Blackwell, vol. 55(2‐3), pages 318-331, May.
    7. Peter F. Stadler & Robert Happel, 1995. "Random Field Models for Fitness Landscapes," Working Papers 95-07-069, Santa Fe Institute.
    8. Stephen J. Decanio, 1999. "Estimating The Non‐Environmental Consequences Of Greenhouse Gas Reductions Is Harder Than You Think," Contemporary Economic Policy, Western Economic Association International, vol. 17(3), pages 279-295, July.

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