Résumé en anglais

We first define the notion of approximation chain and then we use it to obtain, in polynomial time, asymptotic approximation ratio of min{κ/μ, [κ′ log(logΔ)]/Δ} (where κ is a fixed positive constant, κ′ is a constant depending on κ, and Δ, μ are the maximum and the average degrees of the graph, respectively). This result essentially improves, from both complexity and approximation quality points of view, the best-known approximation ratio for maximum independent set.