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We consider the classical problem of broadcasting a large message at an optimal rate in a large scale distributed network under the multi-port communication model. In this context, we are interested in both building an overlay network and providing an explicit algorithm for scheduling the communications. From an optimization point of view, we aim both at maximizing the throughput (i.e., the rate at which nodes receive the message) and minimizing the degree of the participating nodes, i.e., the number of TCP connections they must handle simultaneously. The main novelties of our approach are the introduction of this degree constraint and the classification of the set of participating nodes into two parts: open nodes that stay in the open-Internet and “guarded” nodes that lie behind firewalls or NATs. Two guarded nodes cannot communicate directly, but rather need to use an open node as a gateway for transmitting a message. In the case without guarded nodes, we prove that it is possible to reach the optimal throughput, at the price of a quasi-optimal (up to a small additive increase) degree of the participating nodes. In presence of guarded nodes, our main contributions are a closed form formula for the optimal cyclic throughput and the proof that the optimal solution may require arbitrarily large degrees. In the acyclic case, we propose an algorithm that reaches the optimal throughput with low degree. Then, we prove a worst case ratio between the optimal acyclic and cyclic throughput and show through simulations that this ratio is on average very close to 1, what makes acyclic solutions efficient both in terms of throughput maximization and degree minimization. [ABSTRACT FROM AUTHOR]

In this paper, we consider the problem of assigning a set of clients with demands to a set of servers with capacities and degree constraints. The goal is to find an allocation such that the number of clients assigned to a server is smaller than the server's degree and their overall demand is smaller than the server's capacity, while maximizing the overall throughput. This problem has several natural applications in the context of independent tasks scheduling or virtual machines allocation. We consider both the offline (when clients are known beforehand) and the online (when clients can join and leave the system at any time) versions of the problem. We first show that the degree constraint on the maximal number of clients that a server can handle is realistic in many contexts. Then, our main contribution is to prove that even if it makes the allocation problem more difficult (NP-Complete), a very small additive resource augmentation on the servers degree is enough to find in polynomial time a solution that achieves at least the optimal throughput. After a set of theoretical results on the complexity of the offline and online versions of the problem, we propose several other greedy heuristics to solve the online problem and we compare the performance (in terms of throughput) and the cost (in terms of disconnections and reconnections) of all proposed algorithms through a set of extensive simulation results. [ABSTRACT FROM AUTHOR]