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ABSTRACT: Given a sequence A of n real numbers and two positive integers l andk, where
k £ \fracnlk\leq \frac{n}{l}
, we study the problem of locating k disjoint segments ofA, each of length at leastl, such that the sum of their densities is maximized. The best previously known algorithm, due to Bergkvist and Damaschke,
runs in O(nl+k
2
l
2) time. In this paper, we propose an O(n+k
2
llog l)-time algorithm for it. We also give an optimal algorithm for a related problem raised by Lin etal. in 2003, where the goal
is to locate k disjoint maximum-density segments in a given sequence.
Algorithmica 04/2012; 54(1):107-117. · 0.60 Impact Factor
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ABSTRACT: A fundamental problem arising in the evolutionary molecular biology is to discover the locations of gene duplications and multiple gene duplication episodes based on the phylogenetic information. The solutions to the MULTIPLE GENE DUPLICATION problems can provide useful clues to place the gene duplication events onto the locations of a species tree and to expose the multiple gene duplication episodes. In this paper, we study two variations of the MULTIPLE GENE DUPLICATION problems: the EPISODE-CLUSTERING (EC) problem and the MINIMUM EPISODES (ME) problem. For the EC problem, we improve the results of Burleigh et al. with an optimal linear-time algorithm. For the ME problem, on the basis of the algorithm presented by Bansal and Eulenstein, we propose an optimal linear-time algorithm.
IEEE/ACM Transactions on Computational Biology and Bioinformatics 03/2011; · 1.54 Impact Factor
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Inf. Process. Lett. 01/2009; 109:171-174.
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ABSTRACT: CNVDetector is a program for locating copy number variations (CNVs) in a single genome. CNVDetector has several merits: (i) it can deal with the array comparative genomic hybridization data even if the noise is not normally distributed; (ii) it has a linear time kernel; (iii) its parameters can be easily selected; (iv) it evaluates the statistical significance for each CNV calling. AVAILABILITY: CNVDetector (for Windows platform) can be downloaded from http:www.csie.ntu.edu.tw/~kmchao/tools/CNVDetector/. The manual of CNVDetector is also available.
Bioinformatics 11/2008; 24(23):2773-5. · 5.47 Impact Factor
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ABSTRACT: In this work, we obtain the following new results. 1. Given a sequence $D=((h_1,s_1), (h_2,s_2) ..., (h_n,s_n))$ of number pairs, where $s_i>0$ for all $i$, and a number $L_h$, we propose an O(n)-time algorithm for finding an index interval $[i,j]$ that maximizes $\frac{\sum_{k=i}^{j} h_k}{\sum_{k=i}^{j} s_k}$ subject to $\sum_{k=i}^{j} h_k \geq L_h$. 2. Given a sequence $D=((h_1,s_1), (h_2,s_2) ..., (h_n,s_n))$ of number pairs, where $s_i=1$ for all $i$, and an integer $L_s$ with $1\leq L_s\leq n$, we propose an $O(n\frac{T(L_s^{1/2})}{L_s^{1/2}})$-time algorithm for finding an index interval $[i,j]$ that maximizes $\frac{\sum_{k=i}^{j} h_k}{\sqrt{\sum_{k=i}^{j} s_k}}$ subject to $\sum_{k=i}^{j} s_k \geq L_s$, where $T(n')$ is the time required to solve the all-pairs shortest paths problem on a graph of $n'$ nodes. By the latest result of Chan \cite{Chan}, $T(n')=O(n'^3 \frac{(\log\log n')^3}{(\log n')^2})$, so our algorithm runs in subquadratic time $O(nL_s\frac{(\log\log L_s)^3}{(\log L_s)^2})$.
10/2008;
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ABSTRACT: For the \textsc{Minkowski Sum Selection} problem with linear objective functions, we obtain the following results: (1) optimal $O(n\log n)$ time algorithms for $\lambda=1$; (2) $O(n\log^2 n)$ time deterministic algorithms and expected $O(n\log n)$ time randomized algorithms for any fixed $\lambda>1$. For the \textsc{Minkowski Sum Finding} problem with linear objective functions or objective functions of the form $f(x,y)=\frac{by}{ax}$, we construct optimal $O(n\log n)$ time algorithms for any fixed $\lambda\geq 1$.
10/2008;
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ABSTRACT: We present an $\tilde{O}(n^{2.5})$-time algorithm for maintaining the topological order of a directed acyclic graph with $n$ vertices while inserting $m$ edges.
05/2008;
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Theor. Comput. Sci. 01/2008; 407:349-358.
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Algorithms and Computation, 18th International Symposium, ISAAC 2007, Sendai, Japan, December 17-19, 2007, Proceedings; 01/2007
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Algorithms and Computation, 17th International Symposium, ISAAC 2006, Kolkata, India, December 18-20, 2006, Proceedings; 01/2006
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SIGMOD Record. 01/2004; 33:21-26.
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[show abstract]
[hide abstract]
ABSTRACT: Given a sequence A of n real numbers and two positive integers l and k, where
k £ \fracnlk \leq \frac{n}{l}, the problem is to locate k disjoint segments of A, each has length at least l, such that their sum of densities is maximized. The best previously known algorithm, due to Bergkvist and Damaschke [1],
runs in O(nl+k
2
l
2) time. In this paper, we give an O(n+k
2
llogl)-time algorithm.
01/1970: pages 300-307;
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ABSTRACT: Katriel and Bodlaender [Irit Katriel, Hans L. Bodlaender, Online topological ordering, ACM Transactions on Algorithms 2 (3) (2006) 364–379] modify the algorithm proposed by Alpern et al. [Bowen Alpern, Roger Hoover, Barry K. Rosen, Peter F. Sweeney, F. Kenneth Zadeck, Incremental evaluation of computational circuits, in: Proceedings of the First Annual ACM–SIAM Symposium on Discrete Algorithms (SODA), 1990, pp. 32–42] for maintaining the topological order of the n nodes of a directed acyclic graph while inserting m edges and prove that their algorithm runs in O(min{m3/2logn,m3/2+n2logn}) time and has an Ω(m3/2) lower bound. In this paper, we give a tight analysis of their algorithm by showing that it runs in time Θ(m3/2+mn1/2logn)1.
Theoretical Computer Science.
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[show abstract]
[hide abstract]
ABSTRACT: A fundamental problem arising in the evolutionary molecular biology is to discover the locations of gene duplications and multiple gene duplication episodes based on the phylogenetic information. The solutions to the MULTIPLE GENE DUPLICATION problems can provide useful clues to place the gene duplication events onto the locations of a species tree and to expose the multiple gene duplication episodes. In this paper, we study two variations of the MULTIPLE GENE DUPLICATION problems: the EPISODE-CLUSTERING (EC) problem and the MINIMUM EPISODES (ME) problem. For the EC problem, we improve the results of Burleigh et al. with an optimal linear-time algorithm. For the ME problem, on the basis of the algorithm presented by Bansal and Eulenstein, we propose an optimal linear-time algorithm.
IEEE/ACM transactions on computational biology and bioinformatics / IEEE, ACM 8(1):260-5. · 2.25 Impact Factor
