BACKGROUND: 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. Exploring complexity issues is a first step towards devising efficient algorithms. The complexity of the median problem for unichromosomal genomes (permutations) has been settled for both the breakpoint distance and the reversal distance. Although the multichromosomal case has often been assumed to be a simple generalization of the unichromosomal case, it is also a relaxation so that complexity in this context does not follow from existing results, and is open for all distances. 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 and linear chromosomes, showing that the multichromosomal problem is actually easier than the unichromosomal problem. Still other variants of these problems are NP-complete, including the DCJ double distance problem, previously mentioned as an open question. We list the remaining open problems. CONCLUSION: This theoretical study clears up a wide swathe of the algorithmical study of genome rearrangements with multiple multichromosomal genomes.
BACKGROUND: 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. Exploring complexity issues is a first step towards devising efficient algorithms. The complexity of the median problem for unichromosomal genomes (permutations) has been settled for both the breakpoint distance and the reversal distance. Although the multichromosomal case has often been assumed to be a simple generalization of the unichromosomal case, it is also a relaxation so that complexity in this context does not follow from existing results, and is open for all distances. 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 and linear chromosomes, showing that the multichromosomal problem is actually easier than the unichromosomal problem. Still other variants of these problems are NP-complete, including the DCJ double distance problem, previously mentioned as an open question. We list the remaining open problems. CONCLUSION: This theoretical study clears up a wide swathe of the algorithmical study of genome rearrangements with multiple multichromosomal genomes.
Authors: Jean-Marc Aury; Olivier Jaillon; Laurent Duret; Benjamin Noel; Claire Jubin; Betina M Porcel; Béatrice Ségurens; Vincent Daubin; Véronique Anthouard; Nathalie Aiach; Olivier Arnaiz; Alain Billaut; Janine Beisson; Isabelle Blanc; Khaled Bouhouche; Francisco Câmara; Sandra Duharcourt; Roderic Guigo; Delphine Gogendeau; Michael Katinka; Anne-Marie Keller; Roland Kissmehl; Catherine Klotz; France Koll; Anne Le Mouël; Gersende Lepère; Sophie Malinsky; Mariusz Nowacki; Jacek K Nowak; Helmut Plattner; Julie Poulain; Françoise Ruiz; Vincent Serrano; Marek Zagulski; Philippe Dessen; Mireille Bétermier; Jean Weissenbach; Claude Scarpelli; Vincent Schächter; Linda Sperling; Eric Meyer; Jean Cohen; Patrick Wincker Journal: Nature Date: 2006-11-01 Impact factor: 49.962
Authors: Chunfang Zheng; P Kerr Wall; Jim Leebens-Mack; Victor A Albert; Claude dePamphilis; David Sankoff Journal: Comput Syst Bioinformatics Conf Date: 2008
Authors: Ngan Nguyen; Glenn Hickey; Daniel R Zerbino; Brian Raney; Dent Earl; Joel Armstrong; W James Kent; David Haussler; Benedict Paten Journal: J Comput Biol Date: 2015-01-07 Impact factor: 1.479
Authors: Benedict Paten; Mark Diekhans; Dent Earl; John St John; Jian Ma; Bernard Suh; David Haussler Journal: J Comput Biol Date: 2011-03 Impact factor: 1.479