Before revision:  We derive a 3-approximation for the two most commonly used objectives of maximizing the weight of the lightest component or minimizing the weight of the heaviest component . Further, we show how to compute our balanced crown decomposition very efficiently which as an intermediate result yields an improved running time in O(|V||E|) for the well-known (Weighted) q-Expansion Lemma .
After revision:  We derive a 3-approximation for the two most commonly used objectives of maximizing the weight of the lightest component or minimizing the weight of the heaviest component .