Francis Y. L. Chin

The University of Hong Kong, Hong Kong, Hong Kong

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Publications (182)95.74 Total impact

  • Francis Y L Chin, Henry C M Leung, S M Yiu
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    ABSTRACT: Sequence assembling is an important step for bioinformatics study. With the help of next generation sequencing (NGS) technology, high throughput DNA fragment (reads) can be randomly sampled from DNA or RNA molecular sequence. However, as the positions of reads being sampled are unknown, assembling process is required for combining overlapped reads to reconstruct the original DNA or RNA sequence. Compared with traditional Sanger sequencing methods, although the throughput of NGS reads increases, the read length is shorter and the error rate is higher. It introduces several problems in assembling. Moreover, paired-end reads instead of single-end reads can be sampled which contain more information. The existing assemblers cannot fully utilize this information and fails to assemble longer contigs. In this article, we will revisit the major problems of assembling NGS reads on genomic, transcriptomic, metagenomic and metatranscriptomic data. We will also describe our IDBA package for solving these problems. IDBA package has adopted several novel ideas in assembling, including using multiple k, local assembling and progressive depth removal. Compared with existence assemblers, IDBA has better performance on many simulated and real sequencing datasets.
    Science China. Life sciences. 10/2014;
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    ABSTRACT: In this paper, we study 1-space bounded 2-dimensional bin packing and square packing. A sequence of rectangular items (square items) arrive one by one, each item must be packed into a square bin of unit size on its arrival without any information about future items. When packing items, 90∘90∘-rotation is allowed. 1-space bounded means there is only one “active” bin. If the “active” bin cannot accommodate the coming item, it will be closed and a new bin will be opened. The objective is to minimize the total number of bins used for packing all items in the sequence. Our contributions are as follows: For 1-space bounded 2-dimensional bin packing, we propose an online packing algorithm with a tight competitive ratio of 5.06. A lower bound of 3.17 on the competitive ratio is proven. Moreover, we study 1-space bounded square packing, where each item is a square with side length no more than 1. A 4.3-competitive algorithm is achieved, and a lower bound of 2.94 on the competitive ratio is given. All these bounds surpass the previously best known results.
    Theoretical Computer Science 10/2014; · 0.49 Impact Factor
  • Yong Zhang, Francis Y. L. Chin, Hing-Fung Ting
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    ABSTRACT: Given a seller with $k$ types of items, $m$ of each, a sequence of users $\{u_1, u_2,\ldots \}$ arrive one by one. Each user is single-minded, i.e., each user is interested only in a particular bundle of items. The seller must set the price and assign some amount of bundles to each user upon his/her arrival. Bundles can be sold fractionally. Each $u_i$ has his/her value function $v_i(\cdot )$ such that $v_i(x)$ is the highest unit price $u_i$ is willing to pay for $x$ bundles. The objective is to maximize the revenue of the seller by setting the price and amount of bundles for each user. In this paper, we first show that a lower bound of the competitive ratio for this problem is $\Omega (\log h+\log k)$ , where $h$ is the highest unit price to be paid among all users. We then give a deterministic online algorithm, Pricing, whose competitive ratio is $O(\sqrt{k}\cdot \log h\log k)$ . When $k=1$ the lower and upper bounds asymptotically match the optimal result $O(\log h)$ .
    Journal of Global Optimization 02/2014; · 1.31 Impact Factor
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    Yi Wang, Henry Leung, Siu Yiu, Francis Chin
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    ABSTRACT: Taxonomic annotation of reads is an important problem in metagenomic analysis. Existing annotation tools, which rely on the approach of aligning each read to the taxonomic structure, are unable to annotate many reads efficiently and accurately as reads (~100 bp) are short and most of them come from unknown genomes. Previous work has suggested assembling the reads to make longer contigs before annotation. More reads/contigs can be annotated as a longer contig (in Kbp) can be aligned to a taxon even if it is from an unknown species as long as it contains a conserved region of that taxon. Unfortunately existing metagenomic assembly tools are not mature enough to produce long enough contigs. Binning tries to group reads/contigs of similar species together. Intuitively, reads in the same group (cluster) should be annotated to the same taxon and these reads altogether should cover a significant portion of the genome alleviating the problem of short contigs if the quality of binning is high. However, no existing work has tried to use binning results to help solve the annotation problem. This work explores this direction. In this paper, we describe MetaCluster-TA, an assembly-assisted binning-based annotation tool which relies on an innovative idea of annotating binned reads instead of aligning each read or contig to the taxonomic structure separately. We propose the novel concept of the 'virtual contig' (which can be up to 10 Kb in length) to represent a set of reads and then represent each cluster as a set of 'virtual contigs' (which together can be total up to 1 Mb in length) for annotation. MetaCluster-TA can outperform widely-used MEGAN4 and can annotate (1) more reads since the virtual contigs are much longer; (2) more accurately since each cluster of long virtual contigs contains global information of the sampled genome which tends to be more accurate than short reads or assembled contigs which contain only local information of the genome; and (3) more efficiently since there are much fewer long virtual contigs to align than short reads. MetaCluster-TA outperforms MetaCluster 5.0 as a binning tool since binning itself can be more sensitive and precise given long virtual contigs and the binning results can be improved using the reference taxonomic database. MetaCluster-TA can outperform widely-used MEGAN4 and can annotate more reads with higher accuracy and higher efficiency. It also outperforms MetaCluster 5.0 as a binning tool.
    BMC Genomics 01/2014; 15 Suppl 1:S12. · 4.40 Impact Factor
  • Yong Zhang, Francis Y.L. Chin, Hing-Fung Ting
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    ABSTRACT: In this paper, we study the online tree node assignment problem, which is a generalization of the well studied OVSF code assignment problem. Assigned nodes in a complete binary tree must follow the rule that each leaf-to-root path must contain at most one assigned node. At times, it is necessary to swap assigned nodes with unassigned nodes in order to accommodate some new node assignment. The target of this problem is to minimize the number of swaps in satisfying a sequence of node assignments and releases. This problem is fundamental, not only to the OVSF code assignment, but also to other applications, such as buddy memory allocation and hypercube subcube allocation. All the previous solutions to this problem are based on a sorted and compact configuration by assigning the nodes linearly and level by level, ignoring the intrinsic tree property in their assignments. Our contributions are: (1) give the concept of safe assignment, which is proved to be unique for any fixed set of node-assignment requests; (2) an 8-competitive algorithm by holding the safe assignment; and (3) an improved 6-competitive variant of this algorithm. Our algorithms are simple and easy to implement and our contributions represent meaningful improvements over recent results.
    Theoretical Computer Science 01/2014; 518:10–21. · 0.49 Impact Factor
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    ABSTRACT: Since the read lengths of high throughput sequencing (HTS) technologies are short, de novo assembly which plays significant roles in many applications remains a great challenge. Most of the state-of-the-art approaches base on de Bruijn graph strategy and overlap-layout strategy. However, these approaches which depend on k-mers or read overlaps do not fully utilize information of single-end and paired-end reads when resolving branches, e.g. the number and positions of reads supporting each possible extension are not taken into account when resolving branches. We present PERGA (Paired-End Reads Guided Assembler), a novel sequence-reads-guided de novo assembly approach, which adopts greedy-like prediction strategy for assembling reads to contigs and scaffolds. Instead of using single-end reads to construct contig, PERGA uses paired-end reads and different read overlap size thresholds ranging from Omax to Omin to resolve the gaps and branches. Moreover, by constructing a decision model using machine learning approach based on branch features, PERGA can determine the correct extension in 99.7% of cases. When the correct extension cannot be determined, PERGA will try to extend the contigs by all feasible extensions and determine the correct extension by using look ahead technology. We evaluated PERGA on both simulated Illumina data sets and real data sets, and it constructed longer and more correct contigs and scaffolds than other state-of-the-art assemblers IDBA-UD, Velvet, ABySS, SGA and CABOG. Availability: https://github.com/hitbio/PERGA
    Proceedings of the International Conference on Bioinformatics, Computational Biology and Biomedical Informatics; 09/2013
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    ABSTRACT: Abstract High-throughput next-generation sequencing technology provides a great opportunity for analyzing metatranscriptomic data. However, the reads produced by these technologies are short and an assembling step is required to combine the short reads into longer contigs. As there are many repeat patterns in mRNAs from different genomes and the abundance ratio of mRNAs in a sample varies a lot, existing assemblers for genomic data, transcriptomic data, and metagenomic data do not work on metatranscriptomic data and produce chimeric contigs, that is, incorrect contigs formed by merging multiple mRNA sequences. To our best knowledge, there is no assembler designed for metatranscriptomic data. In this article, we introduce an assembler called IDBA-MT, which is designed for assembling reads from metatranscriptomic data. IDBA-MT produces much fewer chimeric contigs (reduce by 50% or more) when compared with existing assemblers such as Oases, IDBA-UD, and Trinity.
    Journal of computational biology: a journal of computational molecular cell biology 07/2013; 20(7):540-50. · 1.69 Impact Factor
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    ABSTRACT: RNA sequencing based on next-generation sequencing technology is effective for analyzing transcriptomes. Like de novo genome assembly, de novo transcriptome assembly does not rely on any reference genome or additional annotation information, but is more difficult. In particular, isoforms can have very uneven expression levels (e.g. 1:100), which make it very difficult to identify low-expressed isoforms. One challenge is to remove erroneous vertices/edges with high multiplicity (produced by high-expressed isoforms) in the de Bruijn graph without removing correct ones with not-so-high multiplicity from low-expressed isoforms. Failing to do so will result in the loss of low-expressed isoforms or having complicated subgraphs with transcripts of different genes mixed together due to erroneous vertices/edges. Contributions: Unlike existing tools, which remove erroneous vertices/edges with multiplicities lower than a global threshold, we use a probabilistic progressive approach to iteratively remove them with local thresholds. This enables us to decompose the graph into disconnected components, each containing a few genes, if not a single gene, while retaining many correct vertices/edges of low-expressed isoforms. Combined with existing techniques, IDBA-Tran is able to assemble both high-expressed and low-expressed transcripts and outperform existing assemblers in terms of sensitivity and specificity for both simulated and real data. http://www.cs.hku.hk/∼alse/idba_tran. chin@cs.hku.hk Supplementary data are available at Bioinformatics online.
    Bioinformatics 07/2013; 29(13):i326-i334. · 5.47 Impact Factor
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    Yong Zhang, Francis Y. L. Chin, Hing-Fung Ting, Xin Han
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    ABSTRACT: In this paper, we study 1-space bounded multi-dimensional bin packing and hypercube packing. A sequence of items arrive over time, each item is a d-dimensional hyperbox (in bin packing) or hypercube (in hypercube packing), and the length of each side is no more than 1. These items must be packed without overlapping into d-dimensional hypercubes with unit length on each side. In d-dimensional space, any two dimensions i and j define a space P ij . When an item arrives, we must pack it into an active bin immediately without any knowledge of the future items, and 90∘-rotation on any plane P ij is allowed. The objective is to minimize the total number of bins used for packing all these items in the sequence. In the 1-space bounded variant, there is only one active bin for packing the current item. If the active bin does not have enough space to pack the item, it must be closed and a new active bin is opened. For d-dimensional bin packing, an online algorithm with competitive ratio 4d is given. Moreover, we consider d-dimensional hypercube packing, and give a 2d+1-competitive algorithm. These two results are the first study on 1-space bounded multi dimensional bin packing and hypercube packing.
    Journal of Combinatorial Optimization 01/2013; 26(2). · 0.59 Impact Factor
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    Yi Wang, Henry C M Leung, S M Yiu, Francis Y L Chin
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    ABSTRACT: Metagenomic binning remains an important topic in metagenomic analysis. Existing unsupervised binning methods for next-generation sequencing (NGS) reads do not perform well on (i) samples with low-abundance species or (ii) samples (even with high abundance) when there are many extremely low-abundance species. These two problems are common for real metagenomic datasets. Binning methods that can solve these problems are desirable. We proposed a two-round binning method (MetaCluster 5.0) that aims at identifying both low-abundance and high-abundance species in the presence of a large amount of noise due to many extremely low-abundance species. In summary, MetaCluster 5.0 uses a filtering strategy to remove noise from the extremely low-abundance species. It separate reads of high-abundance species from those of low-abundance species in two different rounds. To overcome the issue of low coverage for low-abundance species, multiple w values are used to group reads with overlapping w-mers, whereas reads from high-abundance species are grouped with high confidence based on a large w and then binning expands to low-abundance species using a relaxed (shorter) w. Compared to the recent tools, TOSS and MetaCluster 4.0, MetaCluster 5.0 can find more species (especially those with low abundance of say 6× to 10×) and can achieve better sensitivity and specificity using less memory and running time. http://i.cs.hku.hk/~alse/MetaCluster/ chin@cs.hku.hk.
    Bioinformatics 09/2012; 28(18):i356-i362. · 5.47 Impact Factor
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    ABSTRACT: When reconstructing a phylogenetic tree, one common representation for a species is a binary string indicating the existence of some selected genes/proteins. Up until now, all existing methods have assumed the existence of these genes/proteins to be independent. However, in most cases, this assumption is not valid. In this paper, we consider the reconstruction problem by taking into account the dependency of proteins, i.e. protein linkage. We assume that the tree structure and leaf sequences are given, so we need only to find an optimal assignment to the ancestral nodes. We prove that the Phylogenetic Tree Reconstruction with Protein Linkage (PTRPL) problem for three different versions of linkage distance is NP-complete. We provide an efficient dynamic programming algorithm to solve the general problem in O (4 m · n )4 and O (4 m ·( m + n )) time (compared to the straight-forward O (4 m · m · n ) and O (4 m · m 2 · n ) time algorithm), depending on the versions of linkage distance used, where .. stands for the number of species and .. for the number of proteins, i.e. length of binary string. We also argue, by experiments, that trees with higher accuracy can be constructed by using linkage information than by using only hamming distance to measure the differences between the binary strings, thus validating the significance of linkage information.
    Proceedings of the 8th international conference on Bioinformatics Research and Applications; 05/2012
  • Yong Zhang, Francis Y. L. Chin, Hing-Fung Ting
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    ABSTRACT: In this paper, we study the problem of online pricing for bundles of items. Given a seller with k types of items, m of each, a sequence of users {u 1 ,u 2 ,⋯} arrives one by one. Each user is single-minded, i.e., each user is interested only in a particular bundle of items. The seller must set the price and assign some amount of bundles to each user upon his/her arrival. Bundles can be sold fractionally. Each u i has his/her value function v i (·) such that v i (x) is the highest unit price u i is willing to pay for x bundles. The objective is to maximize the revenue of the seller by setting the price and amount of bundles for each user. In this paper, we first show that the lower bound of the competitive ratio for this problem is Ω(logh+logk), where h is the highest unit price to be paid among all users. We then give a deterministic online algorithm, Pricing, whose competitive ratio is O(k·loghlogk). When k=1 the lower and upper bounds asymptotically match the optimal result O(logh).
    Proceedings of the 6th international Frontiers in Algorithmics, and Proceedings of the 8th international conference on Algorithmic Aspects in Information and Management; 05/2012
  • Yu Peng, Henry C M Leung, S M Yiu, Francis Y L Chin
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    ABSTRACT: Next-generation sequencing allows us to sequence reads from a microbial environment using single-cell sequencing or metagenomic sequencing technologies. However, both technologies suffer from the problem that sequencing depth of different regions of a genome or genomes from different species are highly uneven. Most existing genome assemblers usually have an assumption that sequencing depths are even. These assemblers fail to construct correct long contigs. We introduce the IDBA-UD algorithm that is based on the de Bruijn graph approach for assembling reads from single-cell sequencing or metagenomic sequencing technologies with uneven sequencing depths. Several non-trivial techniques have been employed to tackle the problems. Instead of using a simple threshold, we use multiple depthrelative thresholds to remove erroneous k-mers in both low-depth and high-depth regions. The technique of local assembly with paired-end information is used to solve the branch problem of low-depth short repeat regions. To speed up the process, an error correction step is conducted to correct reads of high-depth regions that can be aligned to highconfident contigs. Comparison of the performances of IDBA-UD and existing assemblers (Velvet, Velvet-SC, SOAPdenovo and Meta-IDBA) for different datasets, shows that IDBA-UD can reconstruct longer contigs with higher accuracy. The IDBA-UD toolkit is available at our website http://www.cs.hku.hk/~alse/idba_ud
    Bioinformatics 04/2012; 28(11):1420-8. · 5.47 Impact Factor
  • Yi Wang, Henry C M Leung, S M Yiu, Francis Y L Chin
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    ABSTRACT: Next-generation sequencing (NGS) technologies allow the sequencing of microbial communities directly from the environment without prior culturing. The output of environmental DNA sequencing consists of many reads from genomes of different unknown species, making the clustering together reads from the same (or similar) species (also known as binning) a crucial step. The difficulties of the binning problem are due to the following four factors: (1) the lack of reference genomes; (2) uneven abundance ratio of species; (3) short NGS reads; and (4) a large number of species (can be more than a hundred). None of the existing binning tools can handle all four factors. No tools, including both AbundanceBin and MetaCluster 3.0, have demonstrated reasonable performance on a sample with more than 20 species. In this article, we introduce MetaCluster 4.0, an unsupervised binning algorithm that can accurately (with about 80% precision and sensitivity in all cases and at least 90% in some cases) and efficiently bin short reads with varying abundance ratios and is able to handle datasets with 100 species. The novelty of MetaCluster 4.0 stems from solving a few important problems: how to divide reads into groups by a probabilistic approach, how to estimate the 4-mer distribution of each group, how to estimate the number of species, and how to modify MetaCluster 3.0 to handle a large number of species. We show that Meta Cluster 4.0 is effective for both simulated and real datasets. Supplementary Material is available at www.liebertonline.com/cmb.
    Journal of computational biology: a journal of computational molecular cell biology 02/2012; 19(2):241-9. · 1.69 Impact Factor
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    ABSTRACT: Wireless communication networks based on frequency division multiplexing (FDM in short) play an important role in the field of communications, in which each request can be satisfied by assigning a frequency. To avoid interference, each assigned frequency must be different from the neighboring assigned frequencies. Since frequencies are scarce resources, the main problem in wireless networks is how to fully utilize the given bandwidth of frequencies. In this paper, we consider the online call control problem. Given a fixed bandwidth of frequencies and a sequence of communication requests arriving over time, each request must be either satisfied immediately after its arrival by assigning an available frequency, or rejected. The objective of the call control problem is to maximize the number of accepted requests. We study the asymptotic performance of this problem, i.e., the number of requests in the sequence and the bandwidth of frequencies are very large. In this paper, we give a 7/3-competitive algorithm, say CACO, for the call control problem in cellular networks, improving the previous 2.5-competitive result, and show that CACO is best possible among a class of HYBRID algorithms.
    Information Processing Letters 01/2012; 112:21-25. · 0.49 Impact Factor
  • Yu Peng, Henry C M Leung, S M Yiu, Francis Y L Chin
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    ABSTRACT: Next-generation sequencing techniques allow us to generate reads from a microbial environment in order to analyze the microbial community. However, assembling of a set of mixed reads from different species to form contigs is a bottleneck of metagenomic research. Although there are many assemblers for assembling reads from a single genome, there are no assemblers for assembling reads in metagenomic data without reference genome sequences. Moreover, the performances of these assemblers on metagenomic data are far from satisfactory, because of the existence of common regions in the genomes of subspecies and species, which make the assembly problem much more complicated. We introduce the Meta-IDBA algorithm for assembling reads in metagenomic data, which contain multiple genomes from different species. There are two core steps in Meta-IDBA. It first tries to partition the de Bruijn graph into isolated components of different species based on an important observation. Then, for each component, it captures the slight variants of the genomes of subspecies from the same species by multiple alignments and represents the genome of one species, using a consensus sequence. Comparison of the performances of Meta-IDBA and existing assemblers, such as Velvet and Abyss for different metagenomic datasets shows that Meta-IDBA can reconstruct longer contigs with similar accuracy. Meta-IDBA toolkit is available at our website http://www.cs.hku.hk/~alse/metaidba. chin@cs.hku.hk.
    Bioinformatics 07/2011; 27(13):i94-101. · 5.47 Impact Factor
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    ABSTRACT: With the rapid development of next-generation sequencing techniques, metagenomics, also known as environmental genomics, has emerged as an exciting research area that enables us to analyze the microbial environment in which we live. An important step for metagenomic data analysis is the identification and taxonomic characterization of DNA fragments (reads or contigs) resulting from sequencing a sample of mixed species. This step is referred to as 'binning'. Binning algorithms that are based on sequence similarity and sequence composition markers rely heavily on the reference genomes of known microorganisms or phylogenetic markers. Due to the limited availability of reference genomes and the bias and low availability of markers, these algorithms may not be applicable in all cases. Unsupervised binning algorithms which can handle fragments from unknown species provide an alternative approach. However, existing unsupervised binning algorithms only work on datasets either with balanced species abundance ratios or rather different abundance ratios, but not both. In this article, we present MetaCluster 3.0, an integrated binning method based on the unsupervised top--down separation and bottom--up merging strategy, which can bin metagenomic fragments of species with very balanced abundance ratios (say 1:1) to very different abundance ratios (e.g. 1:24) with consistently higher accuracy than existing methods. MetaCluster 3.0 can be downloaded at http://i.cs.hku.hk/~alse/MetaCluster/.
    Bioinformatics 06/2011; 27(11):1489-95. · 5.47 Impact Factor
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    Yongkai Liu, Defu Zhang, Francis Y.L. Chin
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    ABSTRACT: Constructing a feasible solution, where the focus is on ‘hard’ constraints only, is an important part of solving timetabling problems. For the University Course Timetabling Problem, we propose a heuristic algorithm to schedule events to timeslots based on cliques, each representing a set of events that could be scheduled in the same timeslot, which the algorithm constructs. Our algorithm has been tested on a set of well-known instances, and the experimental results show that our algorithm is efficient and can compete with other effective algorithms.
    Optimization Methods and Software 04/2011; 26(2):281-294. · 0.68 Impact Factor
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    ABSTRACT: Understanding the metabolism of new species (e.g. endophytic fungi that produce fuel) have tremendous impact on human lives. Based on predicted proteins and existing reaction databases, one can construct the metabolic network for the species. Next is to identify critical metabolic pathways from the network. Existing computational techniques identify conserved pathways based on multiple networks of related species, but have the following drawbacks. Some do not rely on additional information, so only locate short (of length at most 5), but not necessarily interesting, conserved paths. The others require extensive information (the complete pathway on one species). In reality, researchers usually know only partial information of a metabolic pathway and may not have a conserved pathway in a related species. The Conserved Metabolic Pathway (CMP) problem is to find conserved pathways from the networks with partial information on the initial substrates and final products of the target pathways. Experimental results show that our algorithm CMPFinder can predict useful metabolic pathways with acceptable accuracy.
    Bioinformatics and Biomedicine Workshops (BIBMW), 2010 IEEE International Conference on; 01/2011
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    ABSTRACT: Given a complete binary tree of heighth, the online tree node assignment problem is to serve a sequence of assignment/release requests, where an assignment request, with an integer parameter0≤i≤h, is served by assigning a (tree) node of level (or height)i and a release request is served by releasing a specified assigned node. The node assignments have to guarantee that no node is assigned to two assignment requests unreleased, and every leaf-to-root path of the tree contains at most one assigned node. With assigned node reassignments allowed, the target of the problem is to minimize the number of assignments/reassignments, i.e., the cost, to serve the whole sequence of requests. This online tree node assignment problem is fundamental to many applications, including OVSF code assignment in WCDMA networks, buddy memory allocation and hypercube subcube allocation. Most of the previous results focus on how to achieve good performance when the same amount of resource is given to both the online and the optimal offline algorithms, i.e., one tree. In this paper, we focus on resource augmentation, where the online algorithm is allowed to use more trees than the optimal offline algorithm. By using different approaches, we give (1) a 1-competitive online algorithm, which uses (h+1)/2 trees and is optimal because (h+1)/2 trees are required by any online algorithm to match the cost of the optimal offline algorithm with one tree; (2) a 2-competitive algorithm with 3h/8+2 trees; (3) an amortized 8/3-competitive algorithm with 11/4 trees; (4) a general amortized (4/3+α)-competitive algorithm with (11/4+4/(3α)) trees, for 0<α≤4/3. KeywordsOnline algorithms–Tree node assignment–Resource augmentation
    Journal of Combinatorial Optimization 01/2011; 22:359-377. · 0.59 Impact Factor

Publication Stats

2k Citations
95.74 Total Impact Points

Institutions

  • 1970–2014
    • The University of Hong Kong
      • Department of Computer Science
      Hong Kong, Hong Kong
  • 2013
    • Shanghai Institutes for Biological Sciences
      Shanghai, Shanghai Shi, China
  • 2011
    • Xiamen University
      • Department of Computer Science
      Xiamen, Fujian, China
    • Hebei University
      Pao-ting-shih, Hebei, China
  • 2008
    • Zhejiang University
      • Department of Mathematics
      Hangzhou, Zhejiang Sheng, China
  • 2006
    • Lands Department of The Government of the Hong Kong Special Administrative Region
      Hong Kong, Hong Kong
  • 2005
    • Japan Advanced Institute of Science and Technology
      KMQ, Ishikawa, Japan
  • 2004
    • Chung-Ang University
      • School of Computer Science and Engineering
      Sŏul, Seoul, South Korea
    • Carnegie Mellon University
      Pittsburgh, Pennsylvania, United States
  • 1995
    • Peking University
      Peping, Beijing, China
  • 1993
    • University of Texas at Dallas
      Richardson, Texas, United States
  • 1984
    • University of Alberta
      • Department of Computing Science
      Edmonton, Alberta, Canada
    • The Chinese University of Hong Kong
      • Department of Computer Science and Engineering
      Hong Kong, Hong Kong