Lower Bounds on the Approximation of the Exemplar Conserved Interval Distance Problem of Genomes

Chen, Zhixiang; Fowler, Richard H.; Fu, Bin; Zhu, Binhai

doi:10.1007/11809678_27

Cited by 13 publications

(6 citation statements)

References 14 publications

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“…Unfortunately, it has been shown that, for each of the above mentioned measures, whatever the considered model (exemplar or maximum matching), the problem becomes NP-hard as soon as duplicates are present in genomes (Bryant, 2000;Blin et al, 2004;Blin and Rizzi, 2005;Chauve et al, 2006); some inapproximability results are known for some special cases (Thach, 2005;Chen et al, 2006aChen et al, , 2006b. Therefore, several heuristic methods have been recently devised to obtain (hopefully) good solutions in a reasonable amount of time Bourque et al, 2005).…”

Section: Introductionmentioning

confidence: 98%

“…breakpoints (Sankoff, 1999;Bryant, 2000;Blin et al, 2004;Goldstein et al, 2004;Chrobak et al, 2005), the number of reversals (Bryant, 2000;El-Mabrouk, 2001, 2002Marron et al, 2004;Chen et al, 2005;Swenson et al, 2005aSwenson et al, , 2005bFu et al, 2006;Waleń, 2006, 2007) the number of conserved intervals (Blin and Rizzi, 2005;Chen et al, 2006a), the number of common intervals (Bourque et al, 2005), and the Maximum Adjacency Disruption Number (MAD) (Sankoff and Haque, 2005). However, in the presence of duplications and for each of the above measures, one has first to disambiguate the data by inferring homologs, that is, a non-ambiguous mapping between the genes of the two genomes.…”

Section: Introductionmentioning

confidence: 98%

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A Pseudo-Boolean Framework for Computing Rearrangement Distances between Genomes with Duplicates

Angibaud

Fertin

Rusu

et al. 2007

Journal of Computational Biology

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Computing genomic distances between whole genomes is a fundamental problem in comparative genomics. Recent researches have resulted in different genomic distance definitions, for example, number of breakpoints, number of common intervals, number of conserved intervals, and Maximum Adjacency Disruption number. Unfortunately, it turns out that, in presence of duplications, most problems are NP-hard, and hence several heuristics have been recently proposed. However, while it is relatively easy to compare heuristics between them, until now very little is known about the absolute accuracy of these heuristics. Therefore, there is a great need for algorithmic approaches that compute exact solutions for these genomic distances. In this paper, we present a novel generic pseudo-boolean approach for computing the exact genomic distance between two whole genomes in presence of duplications, and put strong emphasis on common intervals under the maximum matching model. Of particular importance, we show three heuristics which provide very good results on a well-known public dataset of gamma-Proteobacteria.

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Section: Introductionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 98%

A Pseudo-Boolean Framework for Computing Rearrangement Distances between Genomes with Duplicates

Angibaud

Fertin

Rusu

et al. 2007

Journal of Computational Biology

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“…Duplications can occur at several levels, from duplications of a single gene, to duplication of whole chromosome or even a genome. Calculating rearrangement distance for duplicated genomes is, for most of the rearrangement distances, NP-hard ( [5], [6], [7], [8]), and many of them are APX-hard ( [2], [9], [10], [11], [7]). …”

Section: Introductionmentioning

confidence: 99%

Exact double DCJ distance between circular genomes

Hasic

Gavranović

2011

2011 XXIII International Symposium on Information, Communication and Automation Technologies

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The double cut-and-join (DCJ) operation, or 2-break rearrangement was introduced by Yancopoulos et al. ([1]). Finding DCJ distance between double genomes is NP-hard ([2]). To a pair of regular and all-duplicates genome, having only circular chromosomes, we assign generalized breakpoint graph (introduced by Alekseyev and Pevzner ([3]). We give an algorithm for finding the approximation and exact double DCJ distance. We do this by decomposing GBG into maximum number of alternating, closed trails, using branch-and-bound method.

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“…Unfortunately, it has been shown that, for each of the above mentioned measures, and for each model (exemplar or maximum matching), the problem of finding the non-ambiguous one-to-one mapping that optimizes the studied (dis-)similarity measure becomes NP-hard as soon as duplicates are present in genomes (Bryant, 2000;Blin et al, 2004;Blin and Rizzi, 2005;Blin et al, 2007) ; several inapproximability results are known (Thach, 2005;Chen et al, 2006b;Chen et al, 2006a;Blin et al, 2007;Angibaud et al, 2008), and in some cases, heuristic (hence, not exact) methods have been devised to obtain good solutions in a reasonable amount of time Bourque et al, 2005;Angibaud et al, 2007b).…”

Section: Introductionmentioning

confidence: 99%

Efficient Tools for Computing the Number of Breakpoints and the Number of Adjacencies between Two Genomes with Duplicate Genes

Angibaud

Fertin

Rusu

et al. 2008

Journal of Computational Biology

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Comparing genomes of different species is a fundamental problem in comparative genomics. Recent research has resulted in the introduction of different measures between pairs of genomes: reversal distance, number of breakpoints, number of common or conserved intervals, etc. However, classical methods used for computing such mea- 1 scattered across them. Most approaches to overcome this difficulty are based either on the exemplar model, which keeps exactly one copy in each genome of each duplicated gene, or on the maximum matching model, which keeps as many copies as possible of each duplicated gene. The goal is to find an exemplar matching, respectively a maximum matching, that optimizes the studied measure. Unfortunately, it turns out that, in presence of duplications, this problem for each above-mentioned measure is NP-hard.In this paper, we propose to compute the minimum number of breakpoints and the maximum number of adjacencies between two genomes in presence of duplications using two different approaches. The first one is a (exact) generic 0-1 linear programming approach, while the second is a collection of three heuristics. Each of these approaches is applied on each problem and for each of the following models: exemplar, maximum matching and intermediate model, that we introduce here. All these programs are run on a well-known public benchmark dataset of γ-Proteobacteria, and their performances are discussed.

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Lower Bounds on the Approximation of the Exemplar Conserved Interval Distance Problem of Genomes

Cited by 13 publications

References 14 publications

A Pseudo-Boolean Framework for Computing Rearrangement Distances between Genomes with Duplicates

A Pseudo-Boolean Framework for Computing Rearrangement Distances between Genomes with Duplicates

Exact double DCJ distance between circular genomes

Efficient Tools for Computing the Number of Breakpoints and the Number of Adjacencies between Two Genomes with Duplicate Genes

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