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by Micah Adler, Dan Rubenstein
in Proceedings of the 13th Symposium on Discrete Algorithms, ACM Press/SIAM, New York/Philadelphia
http://www.cs.umass.edu/~micah/pubs/pricing.ps
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Abstract:
In [9], Feigenbaum, Papadimitriou and Shenker initiate the study of pricing algorithms for multicast transmission. In this paper, we build on this work by studying the eect on the complexity of pricing when two practical considerations are incorporated into the network model. In particular, we study a model where the session is oered at a number of dierent rates of transmission, and where there is a cost for enabling multicasting at each node of the network. As a test case for the dierent types of pricing that can occur, we consider a pricing mechanism, called Marginal Cost, that has seen considerable attention in simpler network models. We demonstrate that the details of how multiple rates are provided has a signicant impact on the complexity of pricing. For multiple rates provided via the layered paradigm, we provide a distributed algorithm for computing Marginal Cost eciently in terms of local computation and message complexity. The bit complexity (per edge) of this algorithm depends linearly on the product of the tree height and the number of possible rates. However, we provide two lower bounds on bit complexity, demonstrating that computing Marginal Cost (a) with multiple rates requires a bit complexity that is linear in the number of rates, and (b) with a cost for enabling
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