%. #. #&&, & )&) 12 /31 !%&+ (!$ )&( 12, p.581

M. Sur-la-résolution-desprobì-emes, M. , and M. , Pour cela, nous proposons respectivement les programmes linéaireslinéairesà variables booléennes IC-1OP

A. Et-adjacence-2op, Ces 3 programmes prennent en entrée des ordres partiels : P 1 pour IC-1OP et Adjacence-1OP

. Au-vue-des-résultats, nous remarquons que sans surprise, si p est faible (probabilité d'avoir des g` enes attenants faible) ou si la largeur est grande alors le temps de calcul est plus important. Le paramètre q (probabilité d'avoir des adjacences) ne semble pas affecter le temps de calcul. Du point de vue de la mesure, si p est faible

A. Pour-tester-notre-programme-adjacence-1op and . Qui-maximise-le-nombre-d, adjacences entre un ordre partiel et l'identité, nous utilisons les 19 génomes correspondantsàpondantsà chaque triplet (n, p, q) avec n ? {30; 40; 50; 60; 70; 80; 90}, p ? {0, 7; 0, 9} et q ? {0, 4; 0, 6; 0, 8}. Les r` egles 1 et 3 ontétéontété prises en compte lors de la création de ces programmes, Nous obtenons 779 résultats sur 798 5%) et ce en un peu moins de 2 mois 1

M. , O. Ia, and I. Opt, Nombre d'adjacences adj(C) et nombre de points de cassure pdc(C) pour lesprobì emes opt E , opt, p.100

D. Le-nombre, adjacences adj(C) et le nombre de points de cassure pdc(C) pour le modèle maximum, p.119

D. Le-nombre, adjacences adj(C) et le nombre de points de cassure pdc(C) pour le modèle intermédiaire, p.121

D. Le-nombre, adjacences adj(C) et le nombre de points de cassure pdc(C) pour le modèle exemplaire, p.123

I. Nombres-d-'intervalles-communs-obtenus-par and -. Et-adjacence, 156 'influence de p, de q et de la largeur sur le temps de calcul de Adjacence-1OP159 'influence de p, de q et de la largeur sur le nombre maximal d'adjacences obtenu par Adjacence, p.160

-. Adjacence, 84 adj opt I, p.84

M. Nombre, Maximum des Perturbations d'Adjacences), p.32

P. Parcours-en, 50 PCR (Polymérisation en Cha??neCha??ne) 84 pdc opt I, p.175

.. Pré-couplage and .. Probì-eme-probì-eme-paramétré, 61 Probì eme d'optimisation, p.56

]. A. Bibliographie1, M. Ahmadian, S. Ehn, and . Hober, Pyrosequencing : history, biochemistry and future, Clinica chimica acta, vol.363, pp.83-94, 2006.

S. Angibaud, G. Fertin, I. Rusu, A. Thévenin, and S. Vialette, A Pseudo-boolean Programming Approach for Computing the Breakpoint Distance Between Two Genomes with Duplicate Genes, Proceedings of the 5th RECOMB Comparative Genomics Satellite Workshop, pp.16-29, 2007.
DOI : 10.1007/978-3-540-74960-8_2
URL : https://hal.archives-ouvertes.fr/hal-00417902

S. Angibaud, G. Fertin, I. Rusu, A. Thévenin, and S. Vialette, Efficient Tools for Computing the Number of Breakpoints and the Number of Adjacencies between Two Genomes with Duplicate Genes, Journal of Computational Biology, vol.15, issue.8, pp.1093-1115, 2008.
DOI : 10.1089/cmb.2008.0061
URL : https://hal.archives-ouvertes.fr/hal-00416446

S. Angibaud, G. Fertin, I. Rusu, A. Thévenin, and S. Vialette, On the Approximability of Comparing Genomes with Duplicates, Journal of Graph Algorithms and Applications, vol.13, issue.1, pp.19-53, 2008.
DOI : 10.7155/jgaa.00175
URL : https://hal.archives-ouvertes.fr/hal-00159893

S. Angibaud, G. Fertin, I. Rusu, and S. Vialette, How Pseudo-boolean Programming Can Help Genome Rearrangement Distance Computation, Proceedings of the Fourth RECOMB Comparative Genomics Satellite Workshop (RECOMB-CG), pp.75-86, 2006.
DOI : 10.1007/11864127_7
URL : https://hal.archives-ouvertes.fr/hal-00619848

S. Angibaud, G. Fertin, I. Rusu, and S. Vialette, A Pseudo-Boolean Framework for Computing Rearrangement Distances between Genomes with Duplicates, Journal of Computational Biology, vol.14, issue.4, pp.379-393, 2007.
DOI : 10.1089/cmb.2007.A001

S. Angibaud, G. Fertin, A. Thevenin, and S. Vialette, Pseudo Boolean Programming for Partially Ordered Genomes, p.126, 2009.
DOI : 10.1093/bioinformatics/bti1037
URL : https://hal.archives-ouvertes.fr/hal-00416458

D. A. Bader, B. M. Moret, and M. Yan, A Linear-Time Algorithm for Computing Inversion Distance between Signed Permutations with an Experimental Study, Journal of Computational Biology, vol.8, issue.5, pp.483-491, 2001.
DOI : 10.1089/106652701753216503

V. Bafna and P. A. Pevzner, Sorting by Transpositions, SIAM Journal on Discrete Mathematics, vol.11, issue.2, pp.224-240, 1998.
DOI : 10.1137/S089548019528280X
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.156.1168

A. Bergeron and J. Stoye, On the Similarity of Sets of Permutations and Its Applications to Genome Comparison, Proceedings of the 9th International Computing and Combinatorics Conference (COCOON '03), pp.68-79, 2003.
DOI : 10.1007/3-540-45071-8_9

P. Berman, S. Hannenhalli, and M. Karpinski, 1.375-Approximation Algorithm for Sorting by Reversals, ESA '02 : Proceedings of the 10th Annual European Symposium on Algorithms, pp.200-210, 2002.
DOI : 10.1007/3-540-45749-6_21
URL : https://hal.archives-ouvertes.fr/in2p3-01192634

P. Berman and M. Karpinski, On Some Tighter Inapproximability Results (Extended Abstract), Automata, Languages and Programming, pp.705-735, 1999.
DOI : 10.1007/3-540-48523-6_17

D. , L. Berre, and A. Parrain, A propos de l'extension d'un solveur SAT pour traiter des contraintes pseudo-booléennes, InTroisì eme Journées Francophones de Programmation par Contraintes (JFPC07), pp.38-47, 2007.

G. Blin, E. Blaisy, D. Hermelinz, P. Guillon, M. Blanchette et al., Gene Maps Linearization Using Genomic Rearrangement Distances, Journal of Computational Biology, vol.14, issue.4, pp.394-407, 2007.
DOI : 10.1089/cmb.2007.A002
URL : https://hal.archives-ouvertes.fr/hal-00619755

G. Blin, C. Chauve, and G. Fertin, The breakpoint distance for signed sequences, Proceedings of the first Algorithms and Computational Methods for Biochemical and Evolutionary Networks (CompBioNets), pp.3-16, 2004.
URL : https://hal.archives-ouvertes.fr/hal-00620356

G. Blin, C. Chauve, and G. Fertin, Genes Order and Phylogenetic Reconstruction: Application to ??-Proteobacteria, Proceedings of the 3rd RECOMB Comparative Genomics Satellite Workshop (RECOMB-CG'05), pp.11-20, 2005.
DOI : 10.1007/11554714_2
URL : https://hal.archives-ouvertes.fr/hal-00620362

G. Blin, C. Chauve, G. Fertin, R. Rizzi, and S. Vialette, Comparing Genomes with Duplications: A Computational Complexity Point of View, IEEE/ACM Transactions on Computational Biology and Bioinformatics, vol.4, issue.4, pp.4523-534, 2007.
DOI : 10.1109/TCBB.2007.1069
URL : https://hal.archives-ouvertes.fr/hal-00417720

G. Blin, G. Fertin, F. Sikora, and S. Vialette, The Exemplar Breakpoint Distance for Non-trivial Genomes Cannot Be Approximated, 3rd Annual Workshop on Algorithms and Computation (WALCOM'09), pp.357-368, 2009.
DOI : 10.1093/bioinformatics/15.11.909
URL : https://hal.archives-ouvertes.fr/hal-00416491

M. Bogard, N. Ameziane, and J. Lamoril, Microarray d'ADN et profils d'expression des g` enes :Premì ere partie : concept, fabrication et mise en oeuvre, Immunoanalyse et Biologie Spécialisée, pp.71-88, 1925.

D. Bryant, The complexity of calculating exemplar distances In Comparative Genomics : Empirical and Analytical Approaches to Gene Order Dynamics, Map Alignment , and the Evolution of Gene Families, pp.207-212, 1934.

A. Caprara, Sorting by reversals is difficult, Proceedings of the first annual international conference on Computational molecular biology , RECOMB '97, pp.75-83, 1997.
DOI : 10.1145/267521.267531

M. Chang and F. Wang, Efficient algorithms for the maximum weight clique and maximum weight independent set problems on permutation graphs, Information Processing Letters, vol.43, issue.6, pp.293-295, 1992.
DOI : 10.1016/0020-0190(92)90114-B

C. Chauve, G. Fertin, R. Rizzi, and S. Vialette, Genomes Containing Duplicates Are Hard to Compare, Computational Science ? ICCS 2006, pp.783-790, 2006.
DOI : 10.1007/11758525_105
URL : https://hal.archives-ouvertes.fr/hal-00418260

X. Chen, J. Zheng, Z. Fu, P. Nan, Y. Zhong et al., COMPUTING THE ASSIGNMENT OF ORTHOLOGOUS GENES VIA GENOME REARRANGEMENT, Proceedings of the 3rd Asia-Pacific Bioinformatics Conference
DOI : 10.1142/9781860947322_0037

Z. Chen, B. Fu, J. Xu, B. Yang, Z. Zhao et al., Non-breaking Similarity of Genomes with Gene Repetitions, Proceedings of the 18th Annual Symposium on Combinatorial Pattern Matching (CPM'07), pp.119-130, 2007.
DOI : 10.1007/978-3-540-73437-6_14

Z. Chen, B. Fu, and B. Zhu, The Approximability of the Exemplar Breakpoint Distance Problem, Proceedings of the Second International Conference on Aspects in Information and Management, pp.291-302, 2006.
DOI : 10.1007/11775096_27

S. Cook, The complexity of theorem-proving procedures, Proceedings of the third annual ACM symposium on Theory of computing , STOC '71, pp.151-158, 1971.
DOI : 10.1145/800157.805047

G. B. Dantzig, Origins of the simplex method, History of Scientific Computing, pp.141-151, 1990.

B. Davey and H. Priestley, Introduction to Lattices and order, p.41, 2002.
DOI : 10.1017/CBO9780511809088

J. Delgado, I. Lynce, and V. Manquinho, Computing the Summed Adjacency Disruption Number between Two Genomes with Duplicate Genes Using Pseudo-Boolean Optimization, p.112, 2009.
DOI : 10.1073/pnas.89.14.6575

Z. Dias and J. Meidanis, Sorting by Prefix Transpositions, String Processing and Information Retrieval, pp.463-468, 2002.
DOI : 10.1007/3-540-45735-6_7

T. Dobzansky and A. H. Sturtevant, Inversions in the third chromosome of wild races of drosophila pseudoobscura, and their use in the study of the history of the species, Proceedings of the National Academy of Sciences, p.29, 1936.

T. Dobzansky and A. H. Sturtevant, Inversions in the chromosomes of drosophila pseudoobscura, Genetics, vol.23, issue.28, pp.28-64, 1938.

R. Drmanac, I. Labat, I. Brukner, and R. Crkvenjakov, Sequencing of megabase plus DNA by hybridization: Theory of the method, Genomics, vol.4, issue.2, pp.114-128, 1989.
DOI : 10.1016/0888-7543(89)90290-5

F. Droesbeke, M. Hallin, and C. L. Lefevre, Programmation linéaire par l'exemple. Ellipses, p.62, 1986.

N. Eén and N. Sörensson, Translating pseudo-boolean constraints into SAT translating pseudo-boolean constraints into SAT translating pseudo-boolean constraints into SAT, Journal on Satisfiability Boolean Modeling and Computation, vol.2, issue.130, pp.1-25, 2006.

I. Elias and T. Hartman, A 1.375-Approximation Algorithm for Sorting by Transpositions, IEEE/ACM Transactions on Computational Biology and Bioinformatics, vol.3, issue.4, pp.369-379, 2006.
DOI : 10.1109/TCBB.2006.44
URL : https://hal.archives-ouvertes.fr/hal-00662947

H. Fernau, Parameterized algorithmics : A graph-theoretic approach, Habilitationsschrift, p.78, 2005.

Z. Fu and T. Jiang, Computing the breakpoint distance between partially ordered genomes, Journal of Bioinformatics and Computational, vol.17, issue.44, p.45, 2006.

M. R. Garey and D. S. Johnson, Computers and Intractability : a guide to the theory of NP-completeness, pp.55-64, 1979.

W. Gilbert and A. Maxam, The Nucleotide Sequence of the lac Operator, Proceedings of the National Academy of Sciences, pp.3581-3584, 1973.
DOI : 10.1073/pnas.70.12.3581

A. Goffeau, B. G. Barrell, H. Bussey, R. W. Davis, B. Dujon et al., Life with 6000 Genes, Science, vol.274, issue.5287, pp.274563-567, 1996.
DOI : 10.1126/science.274.5287.546

M. C. Golumbic, Algorithmic Graph Theory and Perfect Graphs, p.80, 1980.

R. E. Gomory, Outline of an algorithm for integer solutions to linear programs, Bulletin of the American Mathematical Society, vol.64, issue.5, pp.275-278, 1958.
DOI : 10.1090/S0002-9904-1958-10224-4

R. E. Green, A. Malaspinas, J. Krause, A. W. Briggs, P. L. Johnson et al., A Complete Neandertal Mitochondrial Genome Sequence Determined by High-Throughput Sequencing, Cell, vol.134, issue.3, pp.416-426, 2008.
DOI : 10.1016/j.cell.2008.06.021

S. Hannenhalli and P. A. Pevzner, Transforming men into mice (polynomial algorithm for genomic distance problem), Proceedings of IEEE 36th Annual Foundations of Computer Science, pp.581-592, 1995.
DOI : 10.1109/SFCS.1995.492588

S. Hannenhalli and P. A. Pevzner, Transforming cabbage into turnip, Proceedings of the twenty-seventh annual ACM symposium on Theory of computing , STOC '95, pp.1-27, 1999.
DOI : 10.1145/225058.225112

A. Genome-initiative, Analysis of the genome sequence of the flowering plant arabidopsis thaliana, Nature, vol.408, issue.6814, pp.796-815, 2000.
DOI : 10.1038/35048692

B. N. Jackson, S. Aluru, and P. S. Schnable, Consensus genetic maps: a graph theoretic approach, 2005 IEEE Computational Systems Bioinformatics Conference (CSB'05), pp.35-43, 2005.
DOI : 10.1109/CSB.2005.26

B. N. Jackson, P. S. Schnable, and S. Aluru, Consensus Genetic Maps as Median Orders from Inconsistent Sources, IEEE/ACM Transactions on Computational Biology and Bioinformatics, vol.5, issue.2, pp.161-171, 2008.
DOI : 10.1109/TCBB.2007.70221
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.521.5575

N. Karmarkar, A new polynomial-time algorithm for linear programming, Combinatorica, vol.244, issue.S, pp.373-395, 1984.
DOI : 10.1007/BF02579150

J. D. Kececioglu and D. Sankoff, Exact and approximation algorithms for sorting by reversals, with application to genome rearrangement, Algorithmica, vol.84, issue.4, pp.180-210, 1995.
DOI : 10.1007/BF01188586

L. Khachyan, Polynomial algorithms in linear programming, USSR Computational Mathematics and Mathematical Physics, vol.20, issue.1, pp.1093-1096, 1979.
DOI : 10.1016/0041-5553(80)90061-0

J. Lamoril, N. Ameziane, J. C. Deybach, P. Bouizegarène, and M. Bogard, Les techniques de s??quen??age de l???ADN??: une r??volution en marche. Premi??re partie, Immuno-analyse & Biologie Sp??cialis??e, vol.23, issue.5, pp.260-279, 2008.
DOI : 10.1016/j.immbio.2008.07.016

E. Lerat, V. Daubin, and N. A. Moran, From gene tree to organismal phylogeny in prokaryotes : the case of ?-proteobacteria, PLoS Biology, vol.1, issue.47, pp.101-109, 2003.

E. Lerat, V. Daubin, H. Ochman, and N. A. Moran, Evolutionary Origins of Genomic Repertoires in Bacteria, PLoS Biology, vol.269, issue.5, p.96, 2005.
DOI : 10.1371/journal.pbio.0030130.t001
URL : https://hal.archives-ouvertes.fr/hal-00427770

W. Li, Z. Gu, H. Wang, and A. Nekrutenko, Evolutionary analyses of the human genome, Nature, vol.12, issue.6822, pp.847-849, 2001.
DOI : 10.1038/35057039

A. Louis, E. Ollivier, J. Aude, and J. L. Risler, Massive Sequence Comparisons as a Help in Annotating Genomic Sequences, Genome Research, vol.11, issue.7, pp.1296-1303, 1923.
DOI : 10.1101/gr.GR-1776R

V. M. Manquinho and J. Marques-silva, On using cutting planes in pseudo-boolean optimization. Satisfiability, Boolean Modeling and Computation, pp.209-219, 2006.

M. Marron, K. M. Swenson, and B. M. Moret, Genomic Distances under Deletions and Insertions, Theoretical Computer Science, vol.325, issue.3, pp.347-360, 2004.
DOI : 10.1016/j.tcs.2004.02.039
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.57.8269

C. Mathé, M. F. Sagot, T. Schiex, and P. Rouzé, Current methods of gene prediction, their strengths and weaknesses, Nucleic Acids Research, vol.30, issue.19, pp.4103-4117, 2002.
DOI : 10.1093/nar/gkf543

M. Nakano, N. Nakai, H. Kurita, J. Komatsu, K. Takashima et al., Single-molecule reverse transcription polymerase chain reaction using water-in-oil emulsion, Journal of Bioscience and Bioengineering, vol.99, issue.3, pp.293-295, 2005.
DOI : 10.1263/jbb.99.293

C. T. Nguyen, Y. C. Tay, and L. Zhang, Divide-and-conquer approach for the exemplar breakpoint distance, Bioinformatics, vol.21, issue.10, pp.2171-2176, 1938.
DOI : 10.1093/bioinformatics/bti327

C. H. Papadimitriou and K. Steiglitz, Combinatorial optimization : algorithms and complexity, p.60, 1982.

C. Davies, B. Médigue, and . Adler, Genome sequence of the saprophyte leptospira biflexa provides insights into the evolution of leptospira and the pathogenesis of leptospirosis, PLoS ONE, vol.3, issue.2, pp.1607-125, 2008.

F. Sanger, G. M. Air, B. G. Barrell, N. L. Brown, A. R. Coulson et al., Nucleotide sequence of bacteriophage phi x174 DNA, Nature, issue.5596, pp.265687-695, 1926.

F. Sanger, S. Nicklen, and A. R. Coulson, DNA sequencing with chain-terminating inhibitors, Proceedings of the National Academy of Sciences, pp.5463-5467, 1924.
DOI : 10.1073/pnas.74.12.5463

D. Sankoff, Mechanismes of genome evolution : models and inference. Bulletin of the International Statistical Institute, pp.461-475, 1989.

D. Sankoff, Edit distance for genome comparison based on non-local operations, Combinatorial Pattern Matching, pp.121-135, 1992.
DOI : 10.1007/3-540-56024-6_10

D. Sankoff, Genome rearrangement with gene families, Bioinformatics, vol.15, issue.11, pp.909-917, 1999.
DOI : 10.1093/bioinformatics/15.11.909
URL : http://bioinformatics.oxfordjournals.org/cgi/content/short/15/11/909

D. Sankoff and M. Blanchette, The median problem for breakpoints in comparative genomics, Proceedings of the Third Internaional Computing and Combinatorics Conference (COCOON), volume 1276 of Lecture Notes in Computer Science, pp.251-263, 1997.
DOI : 10.1007/BFb0045092

D. Sankoff and L. Haque, Power Boosts for Cluster Tests, Proceedings of the 3rd RE- COMB Comparative Genomics Satellite Workshop (RECOMB-CG'05), pp.11-20, 2005.
DOI : 10.1007/11554714_11

D. Sankoff, C. Zheng, and A. Lenert, Reversals of Fortune, Proceedings of the 3rd RECOMB Comparative Genomics Satellite Workshop (RECOMB-CG'05), pp.131-141, 2005.
DOI : 10.1007/11554714_12

A. Schrijver, Theory of Linear and Integer Programming, p.130, 1998.

H. M. Sheini and K. A. Sakallah, Pueblo : A hybrid pseudo-boolean SAT solver. Satisfiability, Boolean Modeling and Computation, pp.155-179, 2006.

J. Tang and B. M. Moret, Phylogenetic Reconstruction from Gene-Rearrangement Data with Unequal Gene Content, Proceedings of Workshop on Algorithms and Data Structures (WADS'03), pp.37-46, 2003.
DOI : 10.1007/978-3-540-45078-8_4

E. Tannier and M. Sagot, Sorting by Reversals in Subquadratic Time, Combinatorial Pattern Matching, pp.1-13, 2004.
DOI : 10.1007/978-3-540-27801-6_1
URL : https://hal.archives-ouvertes.fr/hal-00427659

R. L. Tatusov, N. D. Fedorova, J. D. Jackson, A. R. Jacobs, B. Kiryutin et al., The COG database : an updated version includes eukaryotes, BMC Bioinformatics, vol.4, issue.41, 1923.

A. M. Turing, On computable numbers, with an application to the entscheidungsproblem, Proceedings of the London Mathematical Society, pp.230-265, 1936.

T. Uno and M. Yagiura, Fast Algorithms to Enumerate All Common Intervals of Two Permutations, Algorithmica, vol.26, issue.2, pp.290-309, 2000.
DOI : 10.1007/s004539910014

G. Watterson, W. J. Ewens, T. E. Hall, and A. Morgan, The chromosome inversion problem, Journal of Theoretical Biology, vol.99, issue.1, pp.1-7, 1982.
DOI : 10.1016/0022-5193(82)90384-8

I. V. Yapa, D. Schneiderb, J. Kleinbergc, D. Matthewsd, S. Cartinhourb et al., A graph-theoretic approach to comparing and integrating genetic, physical and sequence-based maps, Genetics, vol.165, pp.2235-2247, 2003.

C. Zheng, A. Lenert, and D. Sankoff, Reversal distance for partially ordered genomes, Bioinformatics, vol.21, issue.Suppl 1, pp.1-7, 2003.
DOI : 10.1093/bioinformatics/bti1037

C. Zheng, A. Lenert, and D. Sankoff, Reversal distance for partially ordered genomes, Bioinformatics, vol.21, issue.Suppl 1, pp.502-508, 2005.
DOI : 10.1093/bioinformatics/bti1037
URL : http://bioinformatics.oxfordjournals.org/cgi/content/short/21/suppl_1/i502