Abstract
We study a product pricing model in social networks where the value a possible buyer (vertex) assigns to a product is influenced by the previous buyers and buying proceeds in discrete, synchronous rounds. Each arc in the social network is weighted with the amount by which the value that the end node of the arc assigns to the product is changed in the following rounds when the starting node buys the product. We show that computing the price generating the maximum revenue for the product seller in this setting is possible in strongly polynomial time if all arc weights are non-negative, but the problem becomes NP-hard when negative arc weights are allowed. Moreover, we show that the optimization version of the problem exhibits the interesting property that it is solvable in pseudopolynomial time but not approximable within any constant factor unless P = NP.
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Krumke, S.O., Schwahn, F.D., Thielen, C. (2014). Being Negative Makes Life NP-hard (for Product Sellers). In: Ferro, A., Luccio, F., Widmayer, P. (eds) Fun with Algorithms. FUN 2014. Lecture Notes in Computer Science, vol 8496. Springer, Cham. https://doi.org/10.1007/978-3-319-07890-8_24
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DOI: https://doi.org/10.1007/978-3-319-07890-8_24
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-07889-2
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