Welfare Maximization with Friends-of-Friends Network Externalities
Online social networks allow the collection of large amounts of data about the influence between users connected by a friendship-like relationship. When distributing items among agents forming a social network, this information allows us to exploit network externalities that each agent receives from his neighbors that get the same item. In this paper we consider Friends-of-Friends (2-hop) network externalities, i.e., externalities that not only depend on the neighbors that get the same item but also on neighbors of neighbors. For these externalities we study a setting where multiple different items are assigned to unit-demand agents. Specifically, we study the problem of welfare maximization under different types of externality functions. Let n be the number of agents and m be the number of items. Our contributions are the following: (1) We show that welfare maximization is APX-hard; we show that even for step functions with 2-hop (and also with 1-hop) externalities it is NP-hard to approximate social welfare better than (1-1/e). (2) On the positive side we present (i) an O(sqrt n)-approximation algorithm for general concave externality functions, (ii) an O(log m)-approximation algorithm for linear externality functions, and (iii) an (1-1/e)/6-approximation algorithm for 2-hop step function externalities. We also improve the result from Bhalgat et al. (2012) for 1-hop step function externalities by giving a (1-1/e)/2-approximation algorithm.
Top- Bhattacharya, Sayan
- Dvořák, Wolfgang
- Henzinger, Monika
- Starnberger, Martin
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Category |
Paper in Conference Proceedings or in Workshop Proceedings (Full Paper in Proceedings) |
Event Title |
32nd Symposium on Theoretical Aspects of Computer Science (STACS 2015) |
Divisions |
Theory and Applications of Algorithms |
Subjects |
Theoretische Informatik |
Event Location |
Munich, Germany |
Event Type |
Conference |
Event Dates |
March, 4 - 7 2015 |
Date |
March 2015 |
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