A New Tight Upper Bound on the Transposition Distance

We study the problem of computing the minimal number of adjacent, non-intersecting block interchanges required to transform a permutation into the identity permutation. In particular, we use the graph of a permutation to compute that number for a particular class of permutations in linear time and space, and derive a new tight upper bound on the so-called transposition distance

Transposition Distance Based On The Algebraic Formalism

In computational biology, genome rearrangements is a field in which we study mutational events affecting large portions of a genome. One such event is the transposition, that changes the position of contiguous blocks of genes inside a chromosome. This event generates the problem of transposition distance, that is to find the minimal number of transpositions transforming one chromosome into another. It is not known whether this problem is -hard or has a polynomial time algorithm. Some approximation algorithms have been proposed in the literature, whose proofs are based on exhaustive analysis of graphical properties of suitable cycle graphs. In this paper, we follow a different, more formal approach to the problem, and present a 1.5-approximation algorithm using an algebraic formalism. Besides showing the feasibility of the approach, the presented algorithm exhibits good results, as our experiments show. © 2008 Springer-Verlag Berlin Heidelberg.5167 LNBI115126Bader, D.A., Moret, B.M.E., Yan, M., A linear-time algorithm for computing inversion distance between signed permutations with an experimental study (2001) Journal of Computational Biology, 8 (5), pp. 483-491Bafna, V., Pevzner, P.A., Sorting by transpositions (1995) Proceedings of the Sixth Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 614-623. , San Francisco, USA, JanuaryBafna, V., Pevzner, P.A., Sorting by transpositions (1998) SIAM Journal on Discrete Mathematics, 11 (2), pp. 224-240Benoît-Gagné, M., Hamel, S.: A new and faster method of sorting by transpositions. In: Ma, B., Zhang, K. (eds.) CPM 2007. LNCS, 4580, pp. 131-141. Springer, Heidelberg (2007)Christie, D.A., Sorting permutations by block-interchanges (1996) Information Processing Letters, 60 (4), pp. 165-169Christie, D.A., (1998) Genome Rearrangement Problems, , PhD thesis, Glasgow UniversityElias, I., Hartman, T.: A 1.375-approximation algorithm for sorting by transpositions. In: Casadio, R., Myers, G. (eds.) WABI 2005. LNCS (LNBI), 3692, pp. 204-215. Springer, Heidelberg (2005)Hannenhalli, S., Pevzner, P.A., Transforming men into mice (polynomial algorithm for genomic distance problem) (1995) Proceedings of the 36th Annual Symposium on Foundations of Computer Science (FOCS, pp. 581-592. , October, IEEE Computer Society Press, Los Alamitos () 1995Hartman, T.: A simpler 1.5-approximation algorithm for sorting by transpositions. In: Baeza-Yates, R., Chávez, E., Crochemore, M. (eds.) CPM 2003. LNCS, 2676, pp. 156-169. Springer, Heidelberg (2003)Hartman, T., Shamir, R.: A simpler and faster 1.5-approximation algorithm for sorting by transpositions. In: Proceedings of CPM 2003, pp. 156-169 (2003) (extended version)Honda, M.I., (2004) Implementation of the algorithm of Hartman for the problem of sorting by transpositions, , Master's thesis, Department of Computer Science, University of Brasilia in portugueseMeidanis, J., Dias, Z., An alternative algebraic formalism for genome rearrangements (2000) Comparative Genomics: Empirical and Analyitical Approaches to Gene Order Dynamics, Map Alignment and Evolution of Gene Families, pp. 213-223. , Sankoff, D, Nadeau, J.H, eds, Kluwer Academic Publishers, Dordrecht NovemberMeidanis, J., Walter, M.E.M.T., Dias, Z., Transposition distance between a permutation and its reverse (1997) Proceedings of the 4th South American Workshop on String Processing (WSP 1997), pp. 70-79. , Baeza-Yates, R, ed, Valparaiso, Chile, pp, Carleton University PressMira, C., Meidanis, J., Algebraic formalism for genome rearrangements (part 1) (2005), Technical Report IC-05-10, Institute of Computing, University of Campinas JuneMira, C.V.G., Meidanis, J., Analysis of sorting by transpositions based on algebraic formalism (2004) The Eighth Annual International Conference on Research in Computational Molecular Biology (RECOMB, , MarchWalter, M.E.M.T., Curado, L.R.A.F., Oliveira, A.G.: Working on the problem of sorting by transpositions on genome rearrangements. In: Baeza-Yates, R., Chávez, E., Crochemore, M. (eds.) CPM 2003. LNCS, 2676, pp. 372-383. Springer, Heidelberg (2003)Walter, M.E.M.T., Dias, Z., Meidanis, J., A new approach for approximating the transposition distance (2000) String Processing and Information Retrieval, pp. 199-208. , SPIREWalter, M.E.M.T., Oliveira, E.T.G., Extending the theory of Bafna and Pevzner for the problem of sorting by transpositions (2002) Tendências em Matemática Aplicada e Computacional - TEMA - SBMAC, 3 (1), pp. 213-222. , in portugueseWalter, M.E.M.T., Soares, L.S.N., Dias, Z., Branch-and-bound algorithms for the problem of sorting by transpositions on genome rearrangements (2006) Proceedings of the 26th Congress of the Brazilian Computer Society, XXXIII Seminário integrado de hardware e software - SEMISH, pp. 69-8

\u201cNEL PROFONDO DEL TEMPO E DEI TRAMONTI\u201d. TRA LE CARTE DI LUCIO PICCOLO: NUCLEI IDEATIVI E PROCESSI COMPOSITIVI DI "PLUMELIA".

Biodiversity crises have led scientists to develop strategies for achieving conservation goals. The underlying principle of these strategies lies in systematic conservation planning (SCP), in which there are at least 2 conflicting objectives, making it a good candidate for multi-objective optimization. Although SCP is typically applied at the species level (or hierarchically higher), it can be used at lower hierarchical levels, such as using alleles as basic units for analysis, for conservation genetics. Here, we propose a method of SCP using a multi-objective approach. We used non-dominated sorting genetic algorithm II in order to identify the smallest set of local populations of Dipteryx alata (baru) (a Brazilian Cerrado species) for conservation, representing the known genetic diversity and using allele frequency information associated with heterozygosity and Hardy-Weinberg equilibrium. We worked in 3 variations for the problem. First, we reproduced a previous experiment, but using a multi-objective approach. We found that the smallest set of populations needed to represent all alleles under study was 7, corroborating the results of the previous study, but with more distinct solutions. In the 2nd and 3rd variations, we performed simultaneous optimization of 4 and 5 objectives, respectively. We found similar but refined results for 7 populations, and a larger portfolio considering intraspecific diversity and persistence with populations ranging from 8-22. This is the first study to apply multi-objective algorithms to an SCP problem using alleles at the population level as basic units for analysis