Before revision:  The proposed method satisfies Pareto optimality, envy-freeness, strategy-proofness, and under an additional mild assumption, also proportionality. We show numerically that our method scales better to large problems than alternative approaches.
After revision:  The proposed method satisfies Pareto optimality, envy-freeness, strategy-proofness, and a notion of sharing incentive for our setting. To the best of our knowledge this is the first mechanism to achieve all four properties in our setting. Furthermore, we show numerically that our method scales better to large problems than alternative approaches.