Sharing the cost of muliticast transmissions (preliminary version)

We invest igate cost-sharing algori thms for mult icast transmission. Economic considerations point to two dist inct mechanisms, marginal costand Shapley value, as the two solutions most appropr ia te in this context. We prove tha t the former has a na tura l a lgori thm that uses only two messages per link of the mult icast tree, while we give evidence tha t the latter requires a quadrat ic total number of messages. We also show tha t the welfare value achieved by an opt imal mult icast tree is NP-ha rd to approximate within any constant factor, even for bounded-degree networks. The lower-bound proof for the Shapley value uses a novel algebraic technique for bounding from below the number of messages exchanged in a dis t r ibuted computa t ion; this technique may prove useful in o ther contexts as well.

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