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23 results on '"Clément Legrand"'

20. Parameterized Complexity of Untangling Knots

Author

Clément Legrand-Duchesne and Ashutosh Rai and Martin Tancer, Legrand-Duchesne, Clément, Rai, Ashutosh, Tancer, Martin, Clément Legrand-Duchesne and Ashutosh Rai and Martin Tancer, Legrand-Duchesne, Clément, Rai, Ashutosh, and Tancer, Martin

Abstract

Deciding whether a diagram of a knot can be untangled with a given number of moves (as a part of the input) is known to be NP-complete. In this paper we determine the parameterized complexity of this problem with respect to a natural parameter called defect. Roughly speaking, it measures the efficiency of the moves used in the shortest untangling sequence of Reidemeister moves. We show that the II^- moves in a shortest untangling sequence can be essentially performed greedily. Using that, we show that this problem belongs to W[P] when parameterized by the defect. We also show that this problem is W[P]-hard by a reduction from Minimum axiom set.

Published
2022
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21. Using Machine Learning to Enhance Clarke and Wright Heuristic

Author

Clément Legrand, Luca Accorsi, Vigo Daniele, Diego Cattaruzza, Marie-Eléonore Kessaci, Laetitia Jourdan, Operational Research, Knowledge And Data (ORKAD), Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 (CRIStAL), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS), University of Bologna/Università di Bologna, Université de Lille-Centrale Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centrale Lille-Centre National de la Recherche Scientifique (CNRS), and University of Bologna

Subjects
[INFO.INFO-RO]Computer Science [cs]/Operations Research [cs.RO], ComputingMilieux_MISCELLANEOUS
Abstract

National audience

Published
2021

22. Kempe Changes in Bounded Treewidth Graphs

Author

Marthe Bonamy, Vincent Delecroix, and Clément Legrand-Duchesne

Subjects
Combinatorics, Treewidth, Polynomial, Sequence, Bounded function, Graph theory, Graph, Exponential function, Mathematics
Abstract

We consider Kempe changes on the k-colourings of a graph on n vertices. If the graph is \((k-1)\)-degenerate, then all its k-colourings are equivalent up to Kempe changes. However, the sequence between two k-colourings that arises from the corresponding proof may be exponential in the number of vertices. An intriguing open question is whether it can be turned polynomial. We prove this to be possible under the stronger assumption that the graph has treewidth at most \(k-1\). Namely, any two k-colourings are equivalent up to \(O(k n^2)\) Kempe changes.

Published
2021
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23. Machine Learning for Multi-Objective Problems

Author

Clément Legrand, Diego Cattaruzza, Laetitia Jourdan, Marie-Eléonore Kessaci, Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 (CRIStAL), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS), Operational Research, Knowledge And Data (ORKAD), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS), Integrated Optimization with Complex Structure (INOCS), Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université libre de Bruxelles (ULB)-Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 (CRIStAL), and INSA Lyon

Subjects
Knowledge Extraction, [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO], Routing Problems, Operational Research, [INFO.INFO-RO]Computer Science [cs]/Operations Research [cs.RO], ComputingMilieux_MISCELLANEOUS, Multi Objective
Abstract

National audience; Machine Learning for Multi-Objective Problems

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