Abstract
As data about genomic architecture accumulates, genomic rearrangements have attracted increasing attention. One of the main rearrangement mechanisms, inversions (also called reversals), was characterized by Hannenhalli and Pevzner and this characterization in turn extended by various authors. The characterization relies on the concepts of breakpoints, cycles, and obstructions colorfully named hurdles and fortresses. In this paper, we study the probability of generating a hurdle in the process of sorting a permutation if one does not take special precautions to avoid them (as in a randomized algorithm, for instance). To do this we revisit and extend the work of Caprara and of Bergeron by providing simple and exact characterizations of the probability of encountering a hurdle in a random permutation. Using similar methods we, for the first time, find an asymptotically tight analysis of the probability that a fortress exists in a random permutation.
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References
Bader, D.A., Moret, B.M.E., Yan, M.: A linear-time algorithm for computing inversion distance between signed permutations with an experimental study. J. Comput. Biol. 8(5), 483–491 (2001); A preliminary version appeared in WADS 2001, pp. 365–376
Bergeron, A.: A very elementary presentation of the Hannenhalli–Pevzner theory. Discrete Applied Mathematics 146(2), 134–145 (2005)
Bergeron, A., Chauve, C., Hartman, T., Saint-Onge, K.: On the properties of sequences of reversals that sort a signed permutation. In: JOBIM, 99–108 (June 2002)
Bergeron, A., Stoye, J.: On the similarity of sets of permutations and its applications to genome comparison. In: Warnow, T.J., Zhu, B. (eds.) COCOON 2003. LNCS, vol. 2697, pp. 68–79. Springer, Heidelberg (2003)
Caprara, A.: On the tightness of the alternating-cycle lower bound for sorting by reversals. J. Combin. Optimization 3, 149–182 (1999)
Hannenhalli, S., Pevzner, P.A.: Transforming cabbage into turnip (polynomial algorithm for sorting signed permutations by reversals). In: Proc. 27th Ann. ACM Symp. Theory of Comput. (STOC 1995), pp. 178–189. ACM Press, New York (1995)
Hannenhalli, S., Pevzner, P.A.: Transforming mice into men (polynomial algorithm for genomic distance problems). In: Proc. 36th Ann. IEEE Symp. Foundations of Comput. Sci. (FOCS 1995), pp. 581–592. IEEE Computer Society Press, Piscataway (1995)
Kaplan, H., Verbin, E.: Efficient data structures and a new randomized approach for sorting signed permutations by reversals. In: Baeza-Yates, R., Chávez, E., Crochemore, M. (eds.) CPM 2003. LNCS, vol. 2676, pp. 170–185. Springer, Heidelberg (2003)
Sankoff, D., Haque, L.: The distribution of genomic distance between random genomes. J. Comput. Biol. 13(5), 1005–1012 (2006)
Sturtevant, A.H., Beadle, G.W.: The relation of inversions in the x-chromosome of drosophila melanogaster to crossing over and disjunction. Genetics 21, 554–604 (1936)
Sturtevant, A.H., Dobzhansky, Th.: Inversions in the third chromosome of wild races of drosophila pseudoobscura and their use in the study of the history of the species. Proc. Nat’l Acad. Sci., USA 22, 448–450 (1936)
Tannier, E., Sagot, M.: Sorting by reversals in subquadratic time. In: Sahinalp, S.C., Muthukrishnan, S.M., Dogrusoz, U. (eds.) CPM 2004. LNCS, vol. 3109, pp. 1–13. Springer, Heidelberg (2004)
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Swenson, K.M., Lin, Y., Rajan, V., Moret, B.M.E. (2008). Hurdles Hardly Have to Be Heeded. In: Nelson, C.E., Vialette, S. (eds) Comparative Genomics. RECOMB-CG 2008. Lecture Notes in Computer Science(), vol 5267. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-87989-3_18
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DOI: https://doi.org/10.1007/978-3-540-87989-3_18
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