Extremal Weighted Path Lengths In Random Binary Search Trees

  • Authors:

  • Rafik Aguech;Nabil Lasmar;Hosam Mahmoud

  • Affiliations:

  • Département de Mathématiques, Faculté des Sciences de Monastir, 5019 Monastir, Tunisia, E-mail: rafikaguech@ipeit.rnu.tn;Département de mathématiques, Institut préparatoire aux études d'ingénieurs de Tunis, IPEIT, Tunis, Tunisia, E-mail: nabillasmar@yahoo.fr;Department of Statistics, The George Washington University, Washington, DC 20052, E-mail: hosam@gwu.edu

  • Venue:
  • Probability in the Engineering and Informational Sciences
  • Year:
  • 2007

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Abstract

We consider weighted path lengths to the extremal leaves in a random binary search tree. When linearly scaled, the weighted path length to the minimal label has Dickman's infinitely divisible distribution as a limit. By contrast, the weighted path length to the maximal label needs to be centered and scaled to converge to a standard normal variate in distribution. The exercise shows that path lengths associated with different ranks exhibit different behaviors depending on the rank. However, the majority of the ranks have a weighted path length with average behavior similar to that of the weighted path to the maximal node.