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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Phase changes in random recursive structures and algorithms

Hsien-Kuei Hwang. Phase changes in random recursive structures and algorithms (a brief survey), Proceedings of the Workshop on Probability with Applications to Finance and Insurance, edited by T. L. Lai, H. Yang and S. P. Yung, World Scientific, pp. 82--97, June 2004. (An English translation based mainly on my Chinese paper published in NSC Natural Science Newsletter, 14(3)(2002), 74-80.)

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Efficient maxima-finding algorithms for random planar samples

Wei-Mei Chen, Hsien-Kuei Hwang, Tsung-Hsi Tsai. Efficient maxima-finding algorithms for random planar samples, Discrete Mathematics and Theoretical Computer Science, 6 (2003), 107--122.

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Berry-Esseen bounds for the number of maxima in planar regions

Zhi-Dong Bai, Hsien-Kuei Hwang, Tsung-Hsi Tsai. Berry-Esseen bounds for the number of maxima in planar regions, Electronic Journal of Probability, 8 (2003), Paper 9, 26 pages. (Errata: Page 4, line 6 (and page 6, line 9): $phi_n(y)$ should be defined
as $phi_n(y) := E(e^{M_ny})/E(e^{N(mu_n,sigma_n^2)y})$; Page 4, line 7 should read $|phi_n^{(m)}(0)| le m! A^m n^{m/6}$.
)

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