Phase changes in random point quadtrees

Hua-Huai Chern, Michael Fuchs, Hsien-Kuei Hwang. Phase changes in random point quadtrees, ACM Transactions on Algorithms, 3:2, Article No. 12 (2007), 51 pages. (Dedicated to the memory of Ching-Zong Wei).

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Profiles of random trees: plane-oriented recursive trees

Hsien-Kuei Hwang. Profiles of random trees: plane-oriented recursive trees, Random Structures and Algorithms, 30:3 (2007), 380-413. An extended abstract of this paper appeared in the special issue of Discrete Mathematics and Theoretical Computer Science for the 2005 International Conference on the Analysis of Algorithms (Barcelona, June 6-10, 2005).

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Width and mode of the profile for random trees of logarithmic height

Luc Devroye, Hsien-Kuei Hwang. Width and mode of the profile for some random trees of logarithmic height, Annals of Applied Probability, 16 (2006), 886-918 (revised version October 22, 2005).

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Partial match queries in random k-d trees

Hua-Huai Chern, Hsien-Kuei Hwang. Partial match queries in random k-d trees, SIAM Journal on Computing, 35:6 (2006) 1440-1466.

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Profiles of random trees: Limit theorems for random recursive trees and binary search trees

Michael Fuchs, Hsien-Kuei Hwang, Ralph Neininger. Profiles of random trees: Limit theorems for random recursive trees and binary search trees, Algorithmica, 46:3-4 (2006), 367-407. (This revised version largely simplifies the calculations of the moments in the previous version, using the approach introduced in this paper. )

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Maxima in hypercubes

Zhi-Dong Bai, Luc Devroye, Hsien-Kuei Hwang, Tsung-Hsi Tsai. Maxima in hypercubes, Random Structures and Algorithms, 27(3) (2005), 290-309.

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Profiles of random trees: correlation and width of random recursive trees and binary search trees

Michael Drmota, Hsien-Kuei Hwang. Profiles of random trees: correlation and width of random recursive trees and binary search trees, Advances in Applied Probability, 37:2 (2005), 321–341. (Corrigendum: Page 323, Corollary 1.2, case (ii): add the condition sign(s_{n,k}) = sign(t_{n,h}).)

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Bimodality and phase transitions in the profile variance of random binary search trees

Michael Drmota, Hsien-Kuei Hwang. Bimodality and phase transitions in the profile variance of random binary search trees, SIAM Journal on Discrete Mathematics, 19:1 (2005), 19-45.

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Limit distribution of the number of consecutive records

Hua-Huai Chern, Hsien-Kuei Hwang. Limit distribution of the number of consecutive records, Random Structures and Algorithms, 26:4 (2005), 404-417.

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Digital sums and divide-and-conquer recurrences: Fourier expansions and absolute convergence

Peter J. Grabner, Hsien-Kuei Hwang. Digital sums and divide-and-conquer recurrences: Fourier expansions and absolute convergence, Constructive Approximation, 21:2 (2005), 149-179.

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