Optimal File Distribution in Peer-to-Peer Networks

We study the problem of distributing a file initially located at a server among a set of peers. Peers who downloaded the file can upload it to other peers. The server and the peers are connected to each other via a core network. The upload and download rates to and from the core are constrained by user and server specific upload and download capacities. Our objective is to minimize the makespan. We derive exact polynomial time algorithms for the case when upload and download capacities per peer and among peers are equal. We show that the problem becomes strongly NP-hard for equal upload and download capacities per peer that may differ among peers. For this case we devise a polynomial time (1 + 2 √ 2)-approximation algorithm. To the best of our knowledge, neither NP-hardness nor approximation algorithms were known before for this