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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 theoreticmethods, we prove that such classes are specified by finite sets of forbidden permutations, are partially well ordered, and have… (More)

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)

The study of patterns in permutations has blossomed these last years: from a combinatorial point of view with the recent proof of the Stanley–Wilf conjecture by Marcus and Tardös, and from an algorithmic one with the development of algorithms for pattern involvement. Although the general pattern involvement problem is NP -hard, some polynomial solutions… (More)

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

In (4), Chaudhuri, Chen, Mihaescu and Rao study algorithmic properties of the tandem duplication random loss model of genome rearrangement, well-known in evolutionary biology. In their model, the cost of one step of duplication-loss of width k is αk for α = 1 or α ≥ 2. In this paper, we study a variant of this model, where the cost of one step of width k is… (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)

Let B be the operation of re-ordering 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 article, we describe an algorithm to determine whether a permutation class C given by a finite basis B of excluded patterns contains a finite number of simple permutations. This is a continuation of the work initiated in [Brignall, Ruškuc, Vatter, Simple permutations: decidability and unavoidable substructures, 2008], and shares several aspects with… (More)

In [8], D. Knuth introduced pattern avoiding permutation classes. Theses classes present nice combinatorial properties, for example 231 avoiding permutations are in one-to-one correspondence with Dyck words. It is then natural to extend this enumerative result to all classes and compute, given B a set of permutations, the generating function S(x) = ∑ snx n… (More)