We investigate the maintenance of overlay networks under massive churn where an adversary may churn a constant fraction an of nodes over the course of O(log(n)) rounds. In particular, the adversary has an almost up-to-date information of the network topology as it can observe an only slightly outdated topology that is at least 2 rounds old. Other than that, we only have the provably minimal restriction that new nodes can only join the network via nodes that have taken part in the network for at least one round. Our contributions are as follows: First, we show that it is impossible to maintain a connected topology if the adversary has up-to-date information about the nodes' connections. As our main result, we present an algorithm that constructs a new overlay — completely independent of all previous overlays — every 2 rounds. Furthermore, each node sends and receives only O(log^3(n)) messages in each round. As part of our solution, we propose the Linearized DeBruijn Swarm (LDS), a highly churn resistant overlay, which will be maintained by the algorithm. However, our approaches can be transferred to a variety of classical P2P topologies where nodes are mapped into the [0, 1)-interval.
Further, @cite_2 build a structured expander, a so-called @math -Graph, which is the union of @math random rings. Their adversary is not only @math -late with regard to communication, it also has access to all nodes' memory and all sent messages after @math . Nodes that are churned out in round @math may remain in the network until some round @math . Thus, it is not immediate.
@cite_2
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This paper addresses the cornerstone family of in distributed computing, and investigates the curious gap between randomized and deterministic solutions under bandwidth restrictions. Our main contribution is in providing tools for derandomizing solutions to local problems, when the @math nodes can only send @math -bit messages in each round of communication. We combine bounded independence, which we show to be sufficient for some algorithms, with the method of conditional expectations and with additional machinery, to obtain the following results. Our techniques give a deterministic maximal independent set (MIS) algorithm in the CONGEST model, where the communication graph is identical to the input graph, in @math rounds, where @math is the diameter of the graph. The best known running time in terms of @math alone is @math , which is super-polylogarithmic, and requires large messages. For the CONGEST model, the only known previous solution is a coloring-based @math -round algorithm, where @math is the maximal degree in the graph. On the way to obtaining the above, we show that in the model, which allows all-to-all communication, there is a deterministic MIS algorithm that runs in @math rounds. , where @math is the maximum degree. When @math , the bound improves to @math and holds also for @math -coloring. In addition, we deterministically construct a @math -spanner with @math edges in @math rounds. For comparison, in the more stringent CONGEST model, the best deterministic algorithm for constructing a @math -spanner with @math edges runs in @math rounds. A novel distributed algorithm for constructing random overlay networks that are composed of d Hamilton cycles is presented. The protocol is completely decentralized as no globally-known server is required. The constructed topologies are expanders with O(log sub d n) diameter with high probability. Our construction is highly scalable because both the processing and the space requirements at each node grow logarithmically with the network size. A new node can join the network in O(log sub d n) time with O(d log sub d n) messages. A node can leave in O(1) time with O(d) messages. The protocol is robust against an offline adversary selecting the sequence of the join and leave operations. We also discuss a layered construction of the random expander networks in which any node can be located in O(log n) time. The random expander networks have applications in community discovery, distributed lookup service, and dynamic connectivity. In this paper, we study the question of how efficiently a collection of interconnected nodes can perform a global computation in the widely studied GOSSIP model of communication. In this model, nodes do not know the global topology of the network, and they may only initiate contact with a single neighbor in each round. This model contrasts with the much less restrictive LOCAL model, where a node may simultaneously communicate with all of its neighbors in a single round. A basic question in this setting is how many rounds of communication are required for the information dissemination problem, in which each node has some piece of information and is required to collect all others. In this paper, we give an algorithm that solves the information dissemination problem in at most @math rounds in a network of diameter @math , withno dependence on the conductance. This is at most an additive polylogarithmic factor from the trivial lower bound of @math , which applies even in the LOCAL model. In fact, we prove that something stronger is true: any algorithm that requires @math rounds in the LOCAL model can be simulated in @math rounds in the GOSSIP model. We thus prove that these two models of distributed computation are essentially equivalent. Given @math wireless transceivers located in a plane, a fundamental problem in wireless communications is to construct a strongly connected digraph on them such that the constituent links can be scheduled in fewest possible time slots, assuming the SINR model of interference. In this paper, we provide an algorithm that connects an arbitrary point set in @math slots, improving on the previous best bound of @math due to Moscibroda. This is complemented with a super-constant lower bound on our approach to connectivity. An important feature is that the algorithms allow for bi-directional (half-duplex) communication. One implication of this result is an improved bound of @math on the worst-case capacity of wireless networks, matching the best bound known for the extensively studied average-case. We explore the utility of oblivious power assignments, and show that essentially all such assignments result in a worst case bound of @math slots for connectivity. This rules out a recent claim of a @math bound using oblivious power. On the other hand, using our result we show that @math slots suffice, where @math is the ratio between the largest and the smallest links in a minimum spanning tree of the points. Our results extend to the related problem of minimum latency aggregation scheduling, where we show that aggregation scheduling with @math latency is possible, improving upon the previous best known latency of @math . We also initiate the study of network design problems in the SINR model beyond strong connectivity, obtaining similar bounds for biconnected and @math -edge connected structures.