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EXTREMAL WEIGHTED PATH LENGTHS IN RANDOM BINARY SEARCH TREES

  • Rafik Aguech (a1), Nabil Lasmar (a2) and Hosam Mahmoud (a3)

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.

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Billingsley, P. (1995). Probability and measure. New York: Wiley.
Devroye, L. (1986). A note on the height of binary search trees. Journal of the ACM 33: 489498.
Devroye, L. (1987). Branching processes in the analysis of the height of trees. Acta Informatica 24: 277298.
Devroye, L. (1988). Applications of the theory of records in the study of random trees. Acta Informatica 26: 123130.
Devroye, L. & Neininger, R. (2004). Distances and finger search in random binary search trees. SIAM Journal on Computing 33: 647658.
Drmota, M. (2001). An analytic approach to the height of binary search trees. Algorithmica 29: 89119.
Drmota, M. (2002). The variance of the height of binary search trees. Theoretical Computer Science 270: 913919.
Hwang, H. & Tsai, T. (2002). Quickselect and Dickman function. Combinatorics, Probability and Computing 11: 353371.
Kemp, R. (1984). Fundamentals of the average case analysis of particular algorithms. Wiley-Teubner Series in Computer Science. New York: Wiley.
Knuth, D. (1998). The art of computer programming. Vol. 3: Sorting and Searching, 2nd ed. Reading, MA: Addison-Wesley.
Mahmoud, H. (1992). Evolution of random search trees. New York: Wiley.
Mahmoud, H. (2000). Sorting: A distribution theory. New York: Wiley.
Mahmoud, H., Modarres, R., & Smythe, R. (1995). Analysis of Quickselect: An algorithm for order statistics. RAIRO: Theoretical Informatics and Its Applications 29: 255276.
Mahmoud, H. & Pittel, B. (1984). On the most probable shape of a search tree grown from a random permutation. SIAM Journal on Algebraic and Discrete Methods 5: 6981.
Pittel, B. (1984). On growing random binary trees. Journal of Mathematical Analysis and Its Applications 103: 461480.
Reed, B. (2003). The height of a random binary search tree. Journal of the Association for Computing Machinery 50: 306332.
Robson, J. (1979). The height of binary search trees. The Australian Computer Journal 11: 151153.

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EXTREMAL WEIGHTED PATH LENGTHS IN RANDOM BINARY SEARCH TREES

  • Rafik Aguech (a1), Nabil Lasmar (a2) and Hosam Mahmoud (a3)

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