WebRTC enables browsers to exchange data directly but the number of possible concurrent connections to a single source is limited. We overcome the limitation by organizing participants in a fat-tree overlay: when the maximum number of connections of a tree node is reached, the new participants connect to the node's children. Our design quickly scales when a large number of participants join in a short amount of time, by relying on a novel scheme that only requires local information to route connection messages: the destination is derived from the hash value of the combined identifiers of the message's source and of the node that is holding the message. The scheme provides deterministic routing of a sequence of connection messages from a single source and probabilistic balancing of newer connections among the leaves. We show that this design puts at least 83 of nodes at the same depth as a deterministic algorithm, can connect a thousand browser windows in 21-55 seconds in a local network, and can be deployed for volunteer computing to tap into 320 cores in less than 30 seconds on a local network to increase the total throughput on the Collatz application by two orders of magnitude compared to a single core.
have originally been proposed to provide high-bandwidth communication between nodes in computing clusters while minimizing the cost of switching hardware @cite_27 . Fat-trees derive their name from the increasing bandwidth requirements on edges closer to the root because they relay traffic for all children in the underlying sub-tree. Fat-trees were later also adopted explicitly or implicitly in , in which nodes connected using Internet protocols are organized in logical networks for efficient communication, to provide, for example, multicast communication @cite_41 @cite_18 .
@cite_41 @cite_27 @cite_18
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This paper proposes the idea of emulating fat-trees in overlays for multi-source multicast applications. Fat-trees are like real trees in that their branches become thicker the closer one gets to the root, thus overcoming the “root bottleneck” of regular trees. We introduce FatNemo, a novel overlay multi-source multicast protocol based on this idea. FatNemo organizes its members into a tree of clusters with cluster sizes increasing closer to the root. It uses bandwidth capacity to decide the highest layer in which a peer can participate, and relies on co-leaders to share the forwarding responsibility and to increase the tree’s resilience to path and node failures. As the size of High Performance Computing clusters grows, so does the probability of interconnect hot spots that degrade the latency and effective bandwidth the network provides. This paper presents a solution to this scalability problem for real life constant bisectional-bandwidth fat-tree topologies. It is shown that maximal bandwidth and cut-through latency can be achieved for MPI global collective traffic. To form such a congestion-free configuration, MPI programs should utilize collective communication, MPI-node-order should be topology aware, and the packet routing should match the MPI communication patterns. First, we show that MPI collectives can be classified into unidirectional and bidirectional shifts. Using this property, we propose a scheme for congestion-free routing of the global collectives in fully and partially populated fat trees running a single job. The no-contention result is then obtained for multiple jobs running on the same fat-tree by applying some job size and placement restrictions. Simulation results of the proposed routing, MPI-node-order and communication patterns show no contention which provides a 40 throughput improvement over previously published results for all-to-all collectives. The past few years have seen a rise in popularity of massively parallel architectures that use fat-trees as their interconnection networks. In this paper we study the communication performance of a parametric family of fat-trees, the k-ary n-trees, built with constant arity switches interconnected in a regular topology. Through simulation on a 4-ary 4-tree with 256 nodes, we analyze some variants of an adaptive algorithm that utilize wormhole routing with one, two and four virtual channels. The experimental results show that the uniform, bit reversal and transpose traffic patterns are very sensitive to the flow control strategy. In all these cases, the saturation points are between 35-40 of the network capacity with one virtual channel, 55-60 with two virtual channels and around 75 with four virtual channels. The complement traffic, a representative of the class of the congestion-free communication patterns, reaches an optimal performance, with a saturation point at 97 of the capacity for all flow control strategies. We study the problem of the amount of information required to perform fast broadcasting in tree networks. The source located at the root of a tree has to disseminate a message to all nodes. In each round each informed node can transmit to one child. Nodes do not know the topology of the tree but an oracle knowing it can give a string of bits of advice to the source which can then pass it down the tree with the source message. The quality of a broadcasting algorithm with advice is measured by its competitive ratio: the worst case ratio, taken over n-node trees, between the time of this algorithm and the optimal broadcasting time in the given tree. Our goal is to find a trade-off between the size of advice and the best competitive ratio of a broadcasting algorithm for n-node trees. We establish such a trade-off with an approximation factor of O(n e ), for an arbitrarily small positive constant e. This is the first communication problem for which a trade-off between the size of advice and the efficiency of the solution is shown for arbitrary size of advice.