On Finding Better Friends in Social Networks

摘要

We study the dynamics of a social network. Each node has to decide locally which other node it wants to befriend, i.e., to which other node it wants to create a connection in order to maximize its welfare, which is defined as the sum of the weights of incident edges. This allows us to model the cooperation between nodes where every node tries to do as well as possible. With the limitation that each node can only have a constant number of friends, we show that every local algorithm is arbitrarily worse than a globally optimal solution. Furthermore, we show that there cannot be a best local algorithm, i.e., for every local algorithm exists a social network in which the algorithm performs arbitrarily worse than some other local algorithm. However, one can combine a number of local algorithms in order to be competitive with the best of them. We also investigate a slightly different valuation variant. Nodes include another node's friends for their valuation. There are scenarios in which this does not converge to a stable state, i.e., the nodes switch friends indefinitely.