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Multichromosomal median and halving problems under different genomic distances

Eric Tannier, Chunfang Zheng, David Sankoff
2009 BMC Bioinformatics  
Results: We settle here the complexity of several genome median and halving problems, including a surprising polynomial result for the breakpoint median and guided halving problems in genomes with circular  ...  Genome median and genome halving are combinatorial optimization problems that aim at reconstructing ancestral genomes as well as the evolutionary events leading from the ancestor to extant species.  ...  DS holds the Canada Research Chair in Mathematical Genomics. Figures 1, 2, 3 and 5 are the work of Sèverine Bérard, used with her kind permission.  ... 
doi:10.1186/1471-2105-10-120 pmid:19386099 pmcid:PMC2683817 fatcat:llnzufiyxbfp5jdwkzmhdlthg4

Multichromosomal Genome Median and Halving Problems [chapter]

Eric Tannier, Chunfang Zheng, David Sankoff
Lecture Notes in Computer Science  
Here we find the complexity of several genome median and halving problems, including a surprising polynomial result for the breakpoint median and guided halving problems in genomes with circular and linear  ...  Genome median and halving problems aim at reconstructing ancestral genomes and the evolutionary events leading from the ancestor to extant species.  ...  DS holds the Canada Research Chair in Mathematical Genomics.  ... 
doi:10.1007/978-3-540-87361-7_1 fatcat:lqqgs5b5frgsnfifapbyz2pz7u

SCJ: A Variant of Breakpoint Distance for Which Sorting, Genome Median and Genome Halving Problems Are Easy [chapter]

Pedro Feijão, João Meidanis
2009 Lecture Notes in Computer Science  
as median and halving.  ...  For the multichromosomal linear genome median problem, this is the first polynomial time algorithm described, since for other breakpoint distances this problem is NP-hard.  ...  problems that are NP-hard under the BP distance, for instance, the multichromosomal linear versions of the genome halving, guided halving and genome median problems.  ... 
doi:10.1007/978-3-642-04241-6_8 fatcat:6o3ukzyplfbvlljgncsto4hnfy

Advances on Genome Duplication Distances [chapter]

Yves Gagnon, Olivier Tremblay Savard, Denis Bertrand, Nadia El-Mabrouk
2010 Lecture Notes in Computer Science  
In the case of a genome G at s containing exactly two copies of each gene, the genome halving problem is to find a perfectly duplicated genome D at d minimizing the rearrangement distance with G.  ...  We generalize the existing exact linear-time algorithm for genome halving to the case of a genome G with missing gene copies.  ...  Conclusion We presented a linear time algorithm to solve the genome halving problem for genomes with missing gene copies.  ... 
doi:10.1007/978-3-642-16181-0_3 fatcat:rdddrafyh5dcpewbopjobdmoqe

Genome Halving and Double Distance with Losses

Olivier Tremblay Savard, Yves Gagnon, Denis Bertrand, Nadia El-Mabrouk
2011 Journal of Computational Biology  
In the case of a genome G at s containing exactly two copies of each gene, the genome halving problem is to find a perfectly duplicated genome D at d minimizing the rearrangement distance with G.  ...  Given a phylogenetic tree involving Whole Genome Duplication events, we contribute to solving the problem of computing the rearrangement and DCJ distances on a branch of the tree linking a duplication  ...  In the case of genome halving, this simplification has been called the Weak Genome Halving Problem (Alekseyev and Pevzner, 2007a) .  ... 
doi:10.1089/cmb.2011.0136 pmid:21899424 fatcat:5vxhkqliobeojj2yi3e64s4xyy

On the Complexity of Rearrangement Problems under the Breakpoint Distance [article]

Jakub Kovac
2013 arXiv   pre-print
The model was introduced by Tannier et al. (2009) who showed that the median problem is solvable in polynomial time in the multichromosomal circular and mixed breakpoint models.  ...  We also show that, in the unichromosomal and the multilinear breakpoint model, the halving problem is NP-hard, thus refuting the conjecture of Tannier et al.  ...  Tomáš Vinař, Comenius University grant UK/121/2011, and by National Scholarship Programme (SAIA), Slovak Republic.  ... 
arXiv:1112.2172v2 fatcat:fnvysatkezadrcisnqu2uw26sa

On the Complexity of Rearrangement Problems under the Breakpoint Distance

Jakub Kováč
2014 Journal of Computational Biology  
We improve the algorithm for the median problem and show that it is equivalent to the problem of finding maximum cardinality nonbipartite matching (under linear reduction).  ...  We also show that in the unichromosomal and the multilinear breakpoint model the halving problem is NP-hard, refuting the conjecture of Tannier et al.  ...  ACKNOWLEDGMENTS The author would like to thank Broňa Brejová and Tomáš Vinař for many constructive comments.  ... 
doi:10.1089/cmb.2013.0004 pmid:24200391 pmcid:PMC3887456 fatcat:guoe2eoir5eppfm3jewcpuuyku

The Problem of Chromosome Reincorporation in DCJ Sorting and Halving [chapter]

Jakub Kováč, Marília D. V. Braga, Jens Stoye
2010 Lecture Notes in Computer Science  
We study two problems in the double cut and join (DCJ) model: sorting -transforming one multilinear genome into another and halving -transforming a duplicated genome into a perfectly duplicated one.  ...  For the restricted sorting problem only a quadratic algorithm was known, whereas the restricted halving problem was stated as open by Tannier, Zheng, and Sankoff.  ...  Tomáš Vinař, VEGA grant 1/0210/10, and the Partnership Stipend from the Bielefeld University.  ... 
doi:10.1007/978-3-642-16181-0_2 fatcat:5wbkuahcdfaobebjqdzspvbiqy

Pathgroups, a dynamic data structure for genome reconstruction problems

Chunfang Zheng
2010 Computer applications in the biosciences : CABIOS  
Motivation: Ancestral gene order reconstruction problems, including the median problem, quartet construction, small phylogeny, guided genome halving and genome aliquoting, are NP hard.  ...  Results: We present a data structure enabling rapid heuristic solution to all these ancestral genome reconstruction problems.  ...  Albert and Ann Stapleton for encouraging the development of the software.  ... 
doi:10.1093/bioinformatics/btq255 pmid:20483815 fatcat:in7vdqqqorgw7dkon3demvctjq

Internal Validation of Ancestral Gene Order Reconstruction in Angiosperm Phylogeny [chapter]

David Sankoff, Chunfang Zheng, P. Kerr Wall, Claude dePamphilis, Jim Leebens-Mack, Victor A. Albert
2008 Lecture Notes in Computer Science  
Using the genome of a related species (the outgroup) to guide the halving of a WGD descendant attenuates this problem.  ...  , use of draft genome sequences in contig form only, incorporation of incomplete sets of homology correspondences among the genomes and addition of large numbers of "singleton" correspondences.  ...  The median problem here is to find the genome, the sum of whose distances from ancestor A, Carica and Vitis is minimal.  ... 
doi:10.1007/978-3-540-87989-3_19 fatcat:2hwk74zqjjctlfaufctpb3ojti

Guided genome halving: hardness, heuristics and the history of the Hemiascomycetes

C. Zheng, Q. Zhu, Z. Adam, D. Sankoff
2008 Bioinformatics  
To resolve this problem, we take account of outgroups, external reference genomes, to guide and narrow down the search.  ...  Results: We improve on a previous, computationally costly, 'brute force' method by adapting the genome halving algorithm of El-Mabrouk and Sankoff so that it rapidly and accurately constructs an ancestor  ...  We also thank Howard Bussey, Eric Tannier and Robert Warren for helpful discussions. D.S. holds the Canada Research Chair in Mathematical Genomics. Conflict of Interest: none declared.  ... 
doi:10.1093/bioinformatics/btn146 pmid:18586750 pmcid:PMC2718624 fatcat:sq2jn3tihve45b73jc6dho6l7a

Issues in the Reconstruction of Gene Order Evolution

David Sankoff, Chunfang Zheng, Adriana Muñoz, Zhenyu Yang, Zaky Adam, Robert Warren, Vicky Choi, Qian Zhu
2010 Journal of Computer Science and Technology  
related genomes.  ...  Multidisciplinary work undertakes to mathematically model these processes and to develop statistical analyses and mathematical algorithms to understand the scrambling in the chromosomes of two or more  ...  problem of partial genome halving.  ... 
doi:10.1007/s11390-010-9301-9 fatcat:x7mt6guq2naktbpre6bogfugmy

Analysis of Gene Order Evolution Beyond Single-Copy Genes [chapter]

Nadia El-Mabrouk, David Sankoff
2012 Msphere  
the problems of orthology, paralogy and synteny block identification.  ...  What was the content and structure of ancestral genomes?  ...  Exercise 3: Use the Genome halving (Section 6.1) and Generalized genome halving (Section 6.2) problems to develop a heuristic for computing the median of one duplicated genome (descendant from a WGD event  ... 
doi:10.1007/978-1-61779-582-4_15 pmid:22407718 fatcat:kerbedfsgrgi5npicdlbd6u4aa

Rearrangements in Phylogenetic Inference: Compare, Model, or Encode? [chapter]

Bernard M. E. Moret, Yu Lin, Jijun Tang
2013 Models and Algorithms for Genome Evolution  
The development of algorithms for distance and median computations led to modelling approaches based on documented biological mechanisms.  ...  Palmer et al. published papers on the evolution of mitochondrial and chloroplast genomes in plants, and D. Sankoff and W.  ...  Sankoff et al. integrated WGD with rearrangements, and introduced the Genome Halving Problem [26] [27] [28] : from the present-day doubled and rearranged genome, recover the pre-doubling ancestral genome  ... 
doi:10.1007/978-1-4471-5298-9_7 fatcat:ssxq63shjrgtpmcr7mukh6yl7e

Rearrangement Problems with Duplicated Genomic Markers [article]

Antoine Thomas
2014 arXiv   pre-print
A major goal of the field is to establish evolutionary relationships within groups of species, in order to infer the topology of an evolutionary tree formed by this group and common ancestors to some of  ...  Understanding the dynamics of genome rearrangements is a major issue of phylogenetics. Phylogenetics is the study of species evolution.  ...  Unlike the genome halving problem, the aim of the 1-tandem halving problem is to find a 1-tandem duplicated genome.  ... 
arXiv:1410.5415v1 fatcat:t3slxmig65a6rihwxgvp66xqlu
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