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1 results

  • One-sided variations on interval trees

  • Part of
  • Yoshiaki Itoh, Hosam M. Mahmoud
  • Journal:
    Journal of Applied Probability / Volume 40 / Issue 3 / September 2003
    Published online by Cambridge University Press:
    14 July 2016, pp. 654-670
    Print publication:
    September 2003

  • The binary interval tree is a random structure that underlies interval division and parking problems. Five incomplete one-sided variants of binary interval trees are considered, providing additional flavors and variations on the main applications. The size of each variant is studied, and a Gaussian tendency is proved in each case via an analytic approach. Differential equations on half scale and delayed differential equations arise and can be solved asymptotically by local expansions and Tauberian theorems. Unlike the binary case, in an incomplete interval tree the size determines most other parameters of interest, such as the height or the internal path length.