Abstract. Könemann, Leonardi, and Schäfer  gave a 2-budget-balanced and groupstrategyproof mechanism for Steiner forest cost-sharing problems. We prove that this mechanism also achieves an O(log 2 k)approximation of the social cost, where k is the number of players. As a consequence, the KLS mechanism has the smallest-possible worst-case efficiency loss, up to constant factors, among all O(1)-budget-balanced Moulin mechanisms for such cost functions. We also extend our results to a more general network design problem.
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