University Paul VerlaineMetz

Montigny-lès-Metz, France

University Paul VerlaineMetz

Montigny-lès-Metz, France

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Couturier J.-F.,University Paul VerlaineMetz | Golovach P.A.,Durham University | Kratsch D.,University Paul VerlaineMetz | Paulusma D.,Durham University
Algorithmica | Year: 2013

The k-Coloring problem is to decide whether a graph can be colored with at most k colors such that no two adjacent vertices receive the same color. The Listk-Coloring problem requires in addition that every vertex u must receive a color from some given set L(u)⊆{1,…,k}. Let Pn denote the path on n vertices, and G+H and rH the disjoint union of two graphs G and H and r copies of H, respectively. For any two fixed integers k and r, we show that Listk-Coloring can be solved in polynomial time for graphs with no induced rP1+P5, hereby extending the result of Hoàng, Kamiński, Lozin, Sawada and Shu for graphs with no induced P5. Our result is tight; we prove that for any graph H that is a supergraph of P1+P5 with at least 5 edges, already List 5-Coloring is NP-complete for graphs with no induced H. © 2013, Springer Science+Business Media New York.


Grasse R.,University Paul VerlaineMetz | Morere Y.,University Paul VerlaineMetz | Pruski A.,University Paul VerlaineMetz
Journal of Intelligent and Robotic Systems: Theory and Applications | Year: 2010

In the few past decades, several international researchers have worked to develop intelligent wheelchairs for the people with reduced mobility. For many of these projects, the structured set of commands is based on a sensor-based command. Many types of commands are available but the final decision is to be made by the user. A former work established a behaviour-based multi-agent form of control ensuring that the user selects the best option for him/her in relation to his/her preferences or requirements. This type of command aims at "merging" this user and his/her machinea kind of symbiotic relationship making the machine more amenable and the command more effective. In this contribution, the approach is based on a curve matching procedure to provide comprehensive assistance to the user. This new agent, using a modelization of the paths that are most frequently used, assists the user during navigation by proposing the direction to be taken when the path has been recognized. This approach will spare the user the effort of determining a new directionwhichmight be amajor benefit in the case of severe disabilities. The approach considered uses particle filtering to implement the recognition of the most frequent paths according to a topological map of the environment. © Springer Science+Business Media B.V. 2010.

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