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                <term xml:lang="en">Diverse routing</term>
                <term xml:lang="en">Shared Risk Link Group</term>
                <term xml:lang="en">colored graph</term>
                <term xml:lang="en">labeled graph</term>
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              <p>The notion of Shared Risk Link Groups (SRLG) has been introduced to capture survivability issues where a set of links of a network fail simultaneously. In this context, the \emph{diverse routing} problem is to find a set of SRLG-disjoint paths between a given pair of end nodes of the network. This problem has been proved $NP$-complete in general~\cite{Hu03} and some polynomial instances have been characterized~\cite{CDP+07}. In this paper, we investigate the diverse routing problem in networks satisfying the \emph{star property}~\cite{LW05}. This property states that an edge may be subject to several SRLGs but all edges subject to a given SRLG are incident to a common node. We first provide counter-examples to the polynomial time algorithm proposed in~\cite{LW05} for computing pairs of SRLG-disjoint paths in networks with the star property, and then prove that this problem is in fact $NP$-hard in the strong sense. More generally, we prove that the diverse routing problem in networks with the star property is $NP$-hard in the strong sense, hard to approximate, and $W[1]$-hard when the parameter is the number of SRLG-disjoint paths. Last, we devise polynomial time algorithms for practically relevant subcases, in particular when the number of SRLG is constant, the maximum degree of the vertices is strictly smaller than 5, and when the network is a directed acyclic graph.</p>
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              <p>La notion de groupe de liens partageant un risque (\emph{Shared Risk Link Group}, (SRLG) a été introduite pour modéliser des problémes de tolérance aux pannes simultanées d'ensembles de liens d'un réseau. Dans ce contexte, le probléme du \emph{routage diversifié} est de trouver un ensemble de chemins SRLG-disjoints entre une paire donnée de n{\oe}uds du réseau. Ce probléme a été prouvé NP-complet en général~\cite{Hu03} et certains cas polynomiaux ont été caractérisés~\cite{CDP+07}. Dans cet article, nous étudions le probléme du routage diversifié dans les réseaux satisfaisants la \emph{propriété d'étoile}~\cite{LW05}. Dans un réseau satisfaisant la propriété d'étoile, un lien peut être affecté par plusieurs SRLGs, mais tous les liens affectés par un même SRLG sont incidents á un même sommet. Nous commençons par donner des contre-exemples á l'algorithme polynomial proposé dans~\cite{LW05} pour le calcul de paires de chemins SRLG-disjoints dans les réseaux satisfaisants la propriété d'étoile. Puis, nous prouvons que ce probléme est en fait NP-difficile au sens fort. Plus généralement, nous montrons que le probléme du routage diversifié dans les réseaux avec la propriété d'étoile est NP-difficile au sens fort, APX-difficile, et W [1]-difficile lorsque le paramétre est le nombre de chemins SRLG-disjoints. Enfin, nous caractérisons de nouvelles instances polynomiales, en particulier lorsque le degré maximum des sommets est 4, ou lorsque le réseau est acyclique.</p>
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