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The goal of this paper is to present a brief survey of a collection of methods and results from the area of combinatorial search [1,8] focusing on graph reconstruction using queries of different type. The study is motivated by applications to genome sequencing.

- Michael H. Albert, M. D. Atkinson, Mathilde Bouvel, Nik Ruškuc, Vincent Vatter
- 2012

A geometric grid class consists of those permutations that can be drawn on a specified set of line segments of slope ±1 arranged in a rectangular pattern governed by a matrix. Using a mixture of geometric and language theoretic methods, we prove that such classes are specified by finite sets of forbidden permutations, are partially well ordered, and have… (More)

- Mathilde Bouvel, Dominique Rossin
- Theor. Comput. Sci.
- 2009

LIAFA Motivations and the model Previous results Combinatorial properties Other questions Outline of the talk 1 Biological motivations and the combinatorial model 2 Previous results: the whole genome duplication-random loss model 3 Some combinatorial properties of the classes C(K , 1) and C(K , p) 4 Other questions to be considered Mathilde Bouvel A variant… (More)

- Mathilde Bouvel, Elisa Pergola
- Theor. Comput. Sci.
- 2010

In this paper, we are interested in the combinatorial analysis of the whole genome duplication-random loss model of genome rearrangement initiated in [8] and [7]. In this model, genomes composed of n genes are modelled by permutations of the set of integers [1..n], that can evolve through duplication-loss steps. It was previously shown that the class of… (More)

In this paper, we give a polynomial (O(n 8)) algorithm for finding a longest common pattern between two permutations of size n given that one is separable. We also give an algorithm for general permutations whose complexity depends on the length of the longest simple permutation involved in one of our permutations.

A sequence of reversals that takes a signed permutation to the identity is perfect if at no step a common interval is broken. Determining a parsimonious perfect sequence of reversals that sorts a signed permutation is NP-hard. Here we show that, despite this worst-case analysis, with probability one, sorting can be done in polynomial time. Further, we find… (More)

Let B be the operation of reordering a sequence by one pass of bubble sort. We completely answer the question of when the inverse image of a principal pattern class under B is a pattern class.

In this paper, we are interested in the combinatorial analysis of the whole genome duplication-random loss model of genome rearrangement initiated in [8] and [7]. In this model, genomes composed of n genes are modeled by permutations of the set of integers [1..n], that can evolve through duplication-loss steps. It was previously shown that the class of… (More)