Résumé en anglais

We study a probabilistic model for graph-problems under vertex-uncertainty. We assume that any vertex v i of the input-graph G has only a probability p i to be present in the final graph to be optimized (i.e., the final instance for the problem tackled will be only a sub-graph of the initial graph). Under this model, the original “deterministic” problem gives rise to a new (deterministic) problem on the same input-graph G, having the same set of feasible solutions as the former one, but its objective function can be very different from the original one, the set of its optimal solutions too. Moreover, this objective function is a sum of 2|V| terms, where V is the vertex-set of G; hence, its computation is not immediately polynomial. We give sufficient conditions for large classes of graph-problems under which objective functions of the probabilistic counterparts are polynomially computable and optimal solutions are well-characterized.