The Approximability of the Exemplar Breakpoint Distance Problem

Chen, Zhixiang; Fu, Bin; Zhu, Binhai

doi:10.1007/11775096_27

Cited by 47 publications

(42 citation statements)

References 17 publications

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“…In Section 3, we prove the APX-hardness of EBD, even for genomes G 1 and G 2 such that occ(G 1 ) = 1 and occ(G 2 ) = 2. This result implies that IBD and MBD are also APX-hard, and extends those of [13].…”

Section: Introductionsupporting

confidence: 60%

“…an intermediate matching, a maximum matching) that induces no breakpoint ? In particular, we extend a result of [13] by proving the problem to be NP-complete in the exemplar model for a new class of instances, we note that the problems are equivalent in the intermediate and the exemplar models and we show that the problem is in P in the maximum matching model. Finally, we focus on a fourth measure, closely related to the number of breakpoints: the number of adjacencies, for which we give several constant ratio approximation algorithms in the maximum matching model, in the case where genomes contain the same number of duplications of each gene.…”

Section: Angibaud Et Al Approximability Of Comparing Genomes With Dusupporting

confidence: 53%

“…Therefore, for sake of abbreviation, we shall denote the corresponding instance simply as Make2I(G 1 , G 2 ) = (D, ω) and forget about the model. the results of [7,10,13]. In a second part of the paper, we have focused on the ZEBD (resp.…”

Section: A 4-approximation For Max-adjmentioning

confidence: 99%

“…intermediate matching, maximum matching) which induces zero breakpoint. In section 4, we study the complexity of ZEBD, ZMBD and ZIBD: in particular, we extend a result of [13] by proving ZEBD to be NP-complete for a new class of instances. We also note that the problems ZEBD and ZIBD are equivalent, and we show that ZMBD is in P.…”

Section: Introductionmentioning

confidence: 99%

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On the Approximability of Comparing Genomes with Duplicates

Angibaud¹,

Fertin²,

Rusu³

et al. 2009

JGAA

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Angibaud et al. Approximability of Comparing Genomes with DuplicatesAbstract A central problem in comparative genomics consists in computing a (dis-)similarity measure between two genomes, e.g. in order to construct a phylogenetic tree. A large number of such measures has been proposed in the recent past: number of reversals, number of breakpoints, number of common or conserved intervals etc. In their initial definitions, all these measures suppose that genomes contain no duplicates. However, we now know that genes can be duplicated within the same genome. One possible approach to overcome this difficulty is to establish a one-to-one correspondence (i.e. a matching) between genes of both genomes, where the correspondence is chosen in order to optimize the studied measure. Then, after a gene relabeling according to this matching and a deletion of the unmatched signed genes, two genomes without duplicates are obtained and the measure can be computed.In this paper, we are interested in three measures (number of breakpoints, number of common intervals and number of conserved intervals) and three models of matching (exemplar, intermediate and maximum matching models). We prove that, for each model and each measure M, computing a matching between two genomes that optimizes M is APX-hard. We show that this result remains true even for two genomes G1 and G2 such that G1 contains no duplicates and no gene of G2 appears more than twice. Therefore, our results extend those of [7,10,13]. Besides, in order to evaluate the possible existence of approximation algorithms concerning the number of breakpoints, we also study the complexity of the following decision problem: is there an exemplarization (resp. an intermediate matching, a maximum matching) that induces no breakpoint ? In particular, we extend a result of [13] by proving the problem to be NP-complete in the exemplar model for a new class of instances, we note that the problems are equivalent in the intermediate and the exemplar models and we show that the problem is in P in the maximum matching model. Finally, we focus on a fourth measure, closely related to the number of breakpoints: the number of adjacencies, for which we give several constant ratio approximation algorithms in the maximum matching model, in the case where genomes contain the same number of duplications of each gene.

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Section: Introductionsupporting

confidence: 60%

Section: Angibaud Et Al Approximability Of Comparing Genomes With Dusupporting

confidence: 53%

Section: A 4-approximation For Max-adjmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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On the Approximability of Comparing Genomes with Duplicates

Angibaud¹,

Fertin²,

Rusu³

et al. 2009

JGAA

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show abstract

“…Moreover, the NP-hardness results in Theorem 1 and Theorem 2 imply that unless NP = P, the corresponding minimization problems of computing the exemplar distance between two genomes do not admit any approximation. We refer to [5,6,4,2,1] for related results.…”

Section: Introductionmentioning

confidence: 99%

The Zero Exemplar Distance Problem

Jiang

2011

Journal of Computational Biology

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Given two genomes with duplicate genes, Zero Exemplar Distance is the problem of deciding whether the two genomes can be reduced to the same genome without duplicate genes by deleting all but one copy of each gene in each genome. Blin, Fertin, Sikora, and Vialette recently proved that Zero Exemplar Distance for monochromosomal genomes is NP-hard even if each gene appears at most two times in each genome, thereby settling an important open question on genome rearrangement in the exemplar model. In this paper, we give a very simple alternative proof of this result. We also study the problem Zero Exemplar Distance for multichromosomal genomes without gene order, and prove the analogous result that it is also NP-hard even if each gene appears at most two times in each genome. For the positive direction, we show that both variants of Zero Exemplar Distance admit polynomial-time algorithms if each gene appears exactly once in one genome and at least once in the other genome. In addition, we present a polynomial-time algorithm for the related problem Exemplar Longest Common Subsequence in the special case that each mandatory symbol appears exactly once in one input sequence and at least once in the other input sequence. This answers an open question of Bonizzoni et al. We also show that Zero Exemplar Distance for multichromosomal genomes without gene order is fixed-parameter tractable if the parameter is the maximum number of chromosomes in each genome.

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

Chen¹,

Fowler²,

et al. 2006

Lecture Notes in Computer Science

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The Approximability of the Exemplar Breakpoint Distance Problem

Cited by 47 publications

References 17 publications

On the Approximability of Comparing Genomes with Duplicates

On the Approximability of Comparing Genomes with Duplicates

The Zero Exemplar Distance Problem

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

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