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 Tsunghsi Tsai

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Average citations per article4.78
Citation Count43
Publication count9
Publication years2002-2017
Available for download1
Average downloads per article59.00
Downloads (cumulative)59
Downloads (12 Months)59
Downloads (6 Weeks)17
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October 2017 ACM Transactions on Algorithms (TALG): Volume 13 Issue 4, December 2017
Publisher: ACM
Citation Count: 0
Downloads (6 Weeks): 17,   Downloads (12 Months): 59,   Downloads (Overall): 59

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Divide-and-conquer recurrences of the form f ( n ) = f (⌊ &fracn2;⌋ ) + f ( ⌈ &fracn2;⌉ ) + g ( n ) ( n ⩾ 2), with g ( n ) and f (1) given, appear very frequently in the analysis of computer algorithms and related areas. ...
Keywords: Analysis of algorithms, master theorems, periodic oscillation, asymptotic approximation, functional equation, additivity, asymptotic linearity, identity, sensitivity analysis, recurrence relation, uniform continuity

April 2015 Advances in Applied Mathematics: Volume 65 Issue C, April 2015
Publisher: Academic Press, Inc.
Citation Count: 0

A detailed study is made of the number of occupied seats in an unfriendly seating scheme with two rows of seats. An unusual identity is derived for the probability generating function, which is itself an asymptotic expansion. The identity implies particularly a local limit theorem with optimal convergence rate. Our ...
Keywords: Central and local limit theorem, Jamming density, Quasi-power theorem, Riccati equation, Stochastic dominance, secondary60D0560F0560E15, primary60C05

January 2012 Computational Geometry: Theory and Applications: Volume 45 Issue 1-2, January, 2012
Publisher: Elsevier Science Publishers B. V.
Citation Count: 1

Simple, two-phase algorithms are devised for finding the maxima of multidimensional point samples, one of the very first problems studied in computational geometry. The algorithms are easily coded and modified for practical needs. The expected complexity of some measures related to the performance of the algorithms is analyzed. We also ...
Keywords: Dominance, Pareto optimality, Maximal points, Multi-objective optimization, Skyline

March 2009 Theoretical Computer Science: Volume 410 Issue 8-10, March, 2009
Publisher: Elsevier Science Publishers Ltd.
Citation Count: 0

Given a function f from {0,1,...,N-1} to {0,1,...,N-1}, we prove that f^m(x), the mth iterate of f at x, can be computed in time O(logN) for each natural number m and each x by using O(N) information that is generated in a preprocessing procedure. Two types of optimal orbit decompositions ...
Keywords: Horton–Strahler number, Fast forward property, Register functions

July 2006 Random Structures & Algorithms: Volume 28 Issue 4, July 2006
Publisher: John Wiley & Sons, Inc.
Citation Count: 5

Limit theorems (including a Berry-Esseen bound) are derived for the number of comparisons taken by the Boyer-Moore algorithm for finding the occurrences of a given pattern in a random text. Previously, only special variants of this algorithm have been analyzed. We also propose a means of computing the limiting constants ...

October 2005 Random Structures & Algorithms: Volume 27 Issue 3, October 2005
Publisher: John Wiley & Sons, Inc.
Citation Count: 8

We derive a Berry-Esseen bound, essentially of the order of the square of the standard deviation, for the number of maxima in random samples from (0, 1) d . The bound is, although not optimal, the first of its kind for the number of maxima in dimensions higher than two. ...

January 2003 Theoretical Computer Science: Volume 290 Issue 3, 3 January 2003
Publisher: Elsevier Science Publishers Ltd.
Citation Count: 6

We derive asymptotic approximations for the sequence f(n) defined recursively by f(n)=min1�j
Keywords: 11B37, Slowly varying functions, Divide-and-conquer, Optimal algorithms, 05A20, 68W40, Power-of-two rules, 68Q25, Recurrence relations

July 2002 Journal of Algorithms - Analysis of algorithms: Volume 44 Issue 1, July 2002
Publisher: Academic Press, Inc.
Citation Count: 9

Cauchy-Euler differential equations surfaced naturally in a number of sorting and searching problems, notably in quicksort and binary search trees and their variations. Asymptotics of coefficients of functions satisfying such equations has been studied for several special cases in the literature. We study in this paper a very general framework ...
Keywords: Cauchy-Euler differential equations, method of moments, asymptotic transfers, binary search trees, convergence in distributions, phase changes, quicksort

July 2002 Combinatorics, Probability and Computing: Volume 11 Issue 4, July 2002
Publisher: Cambridge University Press
Citation Count: 11

We show that the limiting distribution of the number of comparisons used by Hoare's quickselect algorithm when given a random permutation of n elements for finding the m th-smallest element, where m = o ( n ), is the Dickman function. The limiting distribution of the number of exchanges is ...

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