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    Publication
    Towards robust and efficient computation in dynamic Peer-to-Peer networks
    (01-01-2012) ;
    Pandurangan, Gopal
    ;
    Robinson, Peter
    ;
    Upfal, Eli
    Motivated by the need for robust and fast distributed computation in highly dynamic Peer-to-Peer (P2P) networks, we study algorithms for the fundamental distributed agreement problem. P2P networks are highly dynamic networks that experience heavy node churn (i.e., nodes join and leave the network continuously over time). Our goal is to design fast algorithms (running in a small number of rounds) that guarantee, despite high node churn rate, that almost all nodes reach a stable agreement. Our main contributions are randomized distributed algorithms that guarantee stable almost-everywhere agreement with high probability even under high adversarial churn in a polylogarithmic number of rounds. In particular, we present the following results: 1. An O (log 2 n)-round (n is the stable network size) randomized algorithm that achieves almost-everywhere agreement with high probability under up to linear churn per round (i.e., en, for some small constant ε > 0), assuming that the churn is controlled by an oblivious adversary (that has complete knowledge and control of what nodes join and leave and at what time and has unlimited computational power, but is oblivious to the random choices made by the algorithm). 2. An O(log m log3 n)-round randomized algorithm that achieves almost-everywhere agreement with high probability under up to ε√n churn per round (for some small ε > 0), where m is the size of the input value domain, that works even under an adaptive adversary (that also knows the past random choices made by the algorithm). Our algorithms are the first-known, fully-distributed, agreement algorithms that work under highly dynamic settings (i.e., high churn rates per step). Furthermore, they are localized (i.e., do not require any global topological knowledge), simple, and easy to implement. These algorithms can serve as building blocks for implementing other non-trivial distributed computing tasks in dynamic P2P networks. Copyright © SIAM.
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    Publication
    Storage and search in dynamic peer-to-peer networks
    (01-01-2013) ;
    Molla, Anisur Rahaman
    ;
    Morsy, Ehab
    ;
    Pandurangan, Gopal
    ;
    Robinson, Peter
    ;
    Upfal, Eli
    We study robust and efficient distributed algorithms for searching, storing, and maintaining data in dynamic Peer-to-Peer (P2P) networks. P2P networks are highly dynamic networks that experience heavy node churn (i.e., nodes join and leave the network continuously over time). Our goal is to guarantee, despite high node churn rate, that a large number of nodes in the network can store, retrieve, and maintain a large number of data items. Our main contributions are fast randomized distributed algorithms that guarantee the above with high probability even under high adversarial churn. In particular, we present the following main results: 1. A randomized distributed search algorithm that with high probability guarantees that searches from as many as n - o(n) nodes (n is the stable network size) succeed in O(log n)-rounds despite 0(n/ log1+δ n) churn, for any small constant δ > 0, per round. We assume that the churn is controlled by an oblivious adversary (that has complete knowledge and control of what nodes join © 2013 ACM.
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    Publication
    Fast byzantine agreement in dynamic networks
    (11-09-2013) ;
    Pandurangan, Gopal
    ;
    Robinson, Peter
    We study Byzantine agreement in dynamic networks where topology can change from round to round and nodes can also experience heavy churn (i.e., nodes can join and leave the network continuously over time). Our main contributions are randomized distributed algorithms that achieve almost-everywhere Byzantine agreement with high probability even under a large number of adaptively chosen Byzantine nodes and continuous adversarial churn in a number of rounds that is polylogarithmic in n (where n is the stable network size). We show that our algorithms are essentially optimal (up to polylogarithmic factors) with respect to the amount of Byzantine nodes and churn rate that they can tolerate by showing a lower bound. In particular, we present the following results: 1. An O(log3 n) round randomized algorithm to achieve almost-everywhere Byzantine agreement with high probability under a presence of up to O(√n/polylog(n)) Byzantine nodes and up to a churn of O(√n/ polylog(n)) nodes per round. We assume that the Byzantine nodes have knowledge about the entire state of network at every round (including random choices made by all the nodes) and can behave arbitrarily. We also assume that an adversary controls the churn - it has complete knowledge and control of what nodes join and leave and at what time and has unlimited computational power (but is oblivious to the topology changes from round to round). Our algorithm requires only polylogarithmic in n bits to be processed and sent (per round) by each node. 2. We also present an O(log3 n) round randomized algorithm that has same guarantees as the above algorithm, but works even when the connectivity of the network is controlled by an adaptive adversary (that can choose the topology based on the current states of the nodes). However, this algorithm requires up to polynomial in n bits to be processed and sent (per round) by each node. 3. We show that the above bounds are essentially the best possible, if one wants fast (i.e., polylogarithmic run time) algorithms, by showing that any (randomized) algorithm to achieve agreement in a dynamic network controlled by an adversary that can churn up to θ(√n log n) nodes per round should take at least a polynomial number of rounds. Our algorithms are the first-known, fully distributed, Byzantine agreement algorithms in highly dynamic networks. We view our results as a step towards understanding the possibilities and limitations of highly dynamic networks that are subject to malicious behavior by a large number of nodes.