Vincent Bouchitté’s research while affiliated with École Normale Supérieure de Lyon and other places

... To write down the proofs of the following section in a smoother fashion, we restrict (w.l.o.g) tree decompositions to be such that any intersection of two adjacent bags is a minimal separator of the graph. The existence of optimal decompositions with these property is easily seen when defining tree decompositions in terms of triangulations and chordal graphs [31,37]. In this framework, the treewidth of a graph G is the minimum possible maximum clique size in a chordal completion of G. ...

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Automated design of dynamic programming schemes for RNA folding with pseudoknots

... Complexité Dans [BH89] les auteurs conjecturent que le problème de comptage des extensions linéaires d'un ordre sans cycle est de complexité polynomiale. Nous avons montré que ce calcul pouvait se faire en évaluant une formule intégrale de taille linéaire en la taille de l'ordre en entrée. ...

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Concurrent process and combinatorics of increasingly labeled structures : quantitative analysis and random generation algorithms

... 18 V. Bouchitt e, A. Hilali, R. J egou, J.X. Rampon With Proposition 2 and condition (iv) of Theorem 10, we get a new proof of the lower{contiguity of interval orders stated in 4] . Moreover, adding condition (iii), we immediately have: P = (X; P ) is a lattice ii any two element subset of X has an innmum and a supremum in P. The innmum (resp. ...

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Contiguity Orders

... We recall that if y x, then there exists a greedy linear extension that puts x before y [2]. An α-greedy balanced pair in P = (V, ≤) is a pair (x, y) of elements of V such that the ratio of greedy linear extensions of P that put x before y among all greedy linear extensions, denoted GP P (x < y), is in the real interval [α, 1 − α]. ...

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Greedy balanced pairs in $N$-free ordered sets

... l Using the proof of the claim: "For any positive integer m, there is an ordered set with no m-directional representation" given in [S], we show in [2] that for every integer k there exists an interval order which is not k-directional. l These new notions which can model separability problems in computational geometry seem to be an attractive domain for further investigations. ...

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On the Directionality of Interval Orders.

... , h k ; h 1 , . . . , h k } whose only edges are h i h j when there is an arc from h i to h j in H ; also see [1]. If H is transitively oriented, then [4] shows that H is weakly chordal if and only if its bipartite transform is chordal bipartite. ...

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Biclique comparability digraphs of bipartite graphs and minimum ranks of partial matrices

... Maximizing the jump number has many efficient, and some elegant, polynomial time algorithms (this is the bump number problem) [10]. Minimizing the number of jumps is called the jump number problem, and is NP-hard [11,1]. Exact algorithms for jump number have recently been found to run in O(1.824 n ) [5], slightly improving the previous bound of Kratsch and Kratsch's algorithm running in O(1.8638 n ) [6]; the latter also provide a O(1.7593 n )-time algorithm for interval posets. ...

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Greed is good for 2-approximating the jump number for interval posets

... First, by leveraging on classic results from [39], we show that the problem of constructing a ρ-consistent path decomposition of approximately minimum width for the cocomparability graph G ρ of a given partial-order ρ is fixed-parameter tractable with respect to the pathwidth of G ρ . While it was known that the pathwidth and the ρ-consistent pathwidth of G ρ are always the same [3], and that there were fixed-parameter tractable algorithms for computing path decompositions of approximately minimum width due to structural properties of cocomparability graphs [8], the problem of computing such a decomposition satisfying the additional ρ-consistent requirement was open [3]. ...

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Diversity in Kemeny Rank Aggregation: A Parameterized Approach

... Hierarchies and graph problems restricted to graph width parameters [13,52]. Example of specific graphs: Line Graph [417,419], planar graph [201,382,671,24], AT-Free Graph [373,640,122], chordal graph [405,220,129], and sequence Graph [288,402], etc... Algorithms under constraints imposed by graph width parameters [766,486,535,104]. Structural properties of generalized or restricted graph width parameters. ...

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Various Properties of Various Ultrafilters, Various Graph Width Parameters, and Various Connectivity Systems (with survey)

... Investigating the complexity of MWIS in restricted graphs classes led to discovering numerous new tools and techniques in algorithmic graph theory [22,19,16,14]. One of such general techniques is the framework of potential maximal cliques by Bouchitté and Todinca [6,7]. Intuitively speaking, a potential maximal clique (or PMC for short) in a graph G is a bag of a "reasonable" tree decomposition of G (see Section 2 for a formal definition). ...

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Sparse induced subgraphs in $P_7$-free graphs of bounded clique number