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The relationship between randomness and power-law distributed move lengths in random walk algorithms

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  • Sakiyama, Tomoko
  • Gunji, Yukio-Pegio

Abstract

Recently, we proposed a new random walk algorithm, termed the REV algorithm, in which the agent alters the directional rule that governs it using the most recent four random numbers. Here, we examined how a non-bounded number, i.e., “randomness” regarding move direction, was important for optimal searching and power-law distributed step lengths in rule change. We proposed two algorithms: the REV and REV-bounded algorithms. In the REV algorithm, one of the four random numbers used to change the rule is non-bounded. In contrast, all four random numbers in the REV-bounded algorithm are bounded. We showed that the REV algorithm exhibited more consistent power-law distributed step lengths and flexible searching behavior.

Suggested Citation

  • Sakiyama, Tomoko & Gunji, Yukio-Pegio, 2014. "The relationship between randomness and power-law distributed move lengths in random walk algorithms," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 402(C), pages 76-83.
    • Handle: RePEc:eee:phsmap:v:402:y:2014:i:c:p:76-83
    DOI: 10.1016/j.physa.2014.01.060
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    References listed on IDEAS

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    1. G. M. Viswanathan & Sergey V. Buldyrev & Shlomo Havlin & M. G. E. da Luz & E. P. Raposo & H. Eugene Stanley, 1999. "Optimizing the success of random searches," Nature, Nature, vol. 401(6756), pages 911-914, October.
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    Cited by:

    1. Sakiyama, T. & Gunji, Y.P., 2015. "Weber–Fechner relation and Lévy-like searching stemmed from ambiguous experiences," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 438(C), pages 161-168.

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