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Abstract. 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 problem.

We study the problem of distributing a file, initially located at a server, among a set of n nodes. The file is divided into $$m\ge 1$$ m ≥ 1 equally sized packets. After downloading a packet, nodes can upload it to other nodes, possibly to multiple nodes in parallel. Each node, however, may receive each packet from a single source node only. The upload and download rates between nodes are constrained by node- and server-specific upload and download capacities. The objective is to minimize the makespan. This problem has been proposed and analyzed first by Mundinger et al. (J Sched 11:105–120, 2008. 10.1007/s10951-007-0017-9) under the assumption that uploads obey the fair sharing principle, that is, concurrent upload rates from a common source are equal at any point in time. Under this assumption, the authors devised an optimal polynomial time algorithm for the case where the upload capacity of the server and the nodes’ upload and download capacities are all equal. In this work, we drop the fair sharing assumption and derive an exact polynomial time algorithm for the case when upload and download capacities per node and among nodes are equal. We further show that the problem becomes strongly NP-hard for equal upload and download capacities per node that may differ among nodes, even for a single packet. For this case, we devise a polynomial time $$\smash {(1+2\sqrt{2})}$$ ( 1 + 2 2 ) -approximation algorithm. Finally, we devise two polynomial time algorithms with approximation guarantees of 5 and $$2 + \lceil \log _2 \lceil n/m\rceil \rceil /m$$ 2 + ⌈ log 2 ⌈ n / m ⌉ ⌉ / m , respectively, for the general case of m packets.

The article "Broadcasting a file in a communication network", written by Kai-Simon Goetzmann, Tobias Harks and Max Klimm, was originally published electronically on the publisher's internet portal on 11 February 2020 without open access. With the author(s)' decision to opt for Open Choice,