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1. Broadcasting in Noisy Radio Networks

   https://doi.org/10.1145/3087801.3087808  

   Censor-Hillel, Keren; Haeupler, Bernhard; Hershkowitz, D. Ellis; Zuzic, Goran (October 2017, ACM SIGACT-SIGOPS Symposium on Principles of Distributed Computing)

   The widely-studied radio network model [Chlamtac and Kutten, 1985] is a graph-based description that captures the inherent impact of collisions in wireless communication. In this model, the strong assumption is made that node v receives a message from a neighbor if and only if exactly one of its neighbors broadcasts. We relax this assumption by introducing a new noisy radio network model in which random faults occur at senders or receivers. Specifically, for a constant noise parameter p ∈ [0,1), either every sender has probability p of transmitting noise or every receiver of a single transmission in its neighborhood has probability p of receiving noise. We first study single-message broadcast algorithms in noisy radio networks and show that the Decay algorithm [Bar-Yehuda et al., 1992] remains robust in the noisy model while the diameter-linear algorithm of Gasieniec et al., 2007 does not. We give a modified version of the algorithm of Gasieniec et al., 2007 that is robust to sender and receiver faults, and extend both this modified algorithm and the Decay algorithm to robust multi-message broadcast algorithms, broadcasting Ω(1/log n log log n) and Ω(1/log n) messages per round, respectively. We next investigate the extent to which (network) coding improves throughput in noisy radio networks. In particular, we study the coding cap -- the ratio of the throughput of coding to that of routing -- in noisy radio networks. We address the previously perplexing result of Alon et al. 2014 that worst case coding throughput is no better than worst case routing throughput up to constants: we show that the worst case throughput performance of coding is, in fact, superior to that of routing -- by a Θ(log(n)) gap -- provided receiver faults are introduced. However, we show that sender faults have little effect on throughput. In particular, we show that any coding or routing scheme for the noiseless setting can be transformed to be robust to sender faults with only a constant throughput overhead. These transformations imply that the results of Alon et al., 2014 carry over to noisy radio networks with sender faults as well. As a result, if sender faults are introduced then there exist topologies for which there is a Θ(log log n) gap, but the worst case throughput across all topologies is Θ(1/log n) for both coding and routing. 

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2. Communication Lower Bounds for Cryptographic Broadcast Protocols

   Blum, Erica; Boyle, Elette; Cohen, Ran; Liu-Zhang, Chen-Da (October 2023, 37th International Symposium on Distributed Computing (DISC 2023))

   Oshman, Rotem (Ed.)

   Broadcast protocols enable a set of n parties to agree on the input of a designated sender, even in the face of malicious parties who collude to attack the protocol. In the honest-majority setting, a fruitful line of work harnessed randomization and cryptography to achieve low-communication broadcast protocols with sub-quadratic total communication and with "balanced" sub-linear communication cost per party. However, comparatively little is known in the dishonest-majority setting. Here, the most communication-efficient constructions are based on the protocol of Dolev and Strong (SICOMP '83), and sub-quadratic broadcast has not been achieved even using randomization and cryptography. On the other hand, the only nontrivial ω(n) communication lower bounds are restricted to deterministic protocols, or against strong adaptive adversaries that can perform "after the fact" removal of messages. We provide communication lower bounds in this space, which hold against arbitrary cryptography and setup assumptions, as well as a simple protocol showing near tightness of our first bound. - Static adversary. We demonstrate a tradeoff between resiliency and communication for randomized protocols secure against n-o(n) static corruptions. For example, Ω(n⋅ polylog(n)) messages are needed when the number of honest parties is n/polylog(n); Ω(n√n) messages are needed for O(√n) honest parties; and Ω(n²) messages are needed for O(1) honest parties. Complementarily, we demonstrate broadcast with O(n⋅polylog(n)) total communication and balanced polylog(n) per-party cost, facing any constant fraction of static corruptions. - Weakly adaptive adversary. Our second bound considers n/2 + k corruptions and a weakly adaptive adversary that cannot remove messages "after the fact." We show that any broadcast protocol within this setting can be attacked to force an arbitrary party to send messages to k other parties. Our bound implies limitations on the feasibility of balanced low-communication protocols: For example, ruling out broadcast facing 51% corruptions, in which all non-sender parties have sublinear communication locality. 

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3. Smoothed Analysis of Information Spreading in Dynamic Networks

   Dinitz, Michael; Fineman, Jeremy; Gilbert, Seth; Newport, Calvin (October 2022, Leibniz international proceedings in informatics)

   The best known solutions for k-message broadcast in dynamic networks of size n require Ω(nk) rounds. In this paper, we see if these bounds can be improved by smoothed analysis. To do so, we study perhaps the most natural randomized algorithm for disseminating tokens in this setting: at every time step, choose a token to broadcast randomly from the set of tokens you know. We show that with even a small amount of smoothing (i.e., one random edge added per round), this natural strategy solves k-message broadcast in Õ(n+k³) rounds, with high probability, beating the best known bounds for k = o(√n) and matching the Ω(n+k) lower bound for static networks for k = O(n^{1/3}) (ignoring logarithmic factors). In fact, the main result we show is even stronger and more general: given 𝓁-smoothing (i.e., 𝓁 random edges added per round), this simple strategy terminates in O(kn^{2/3}log^{1/3}(n)𝓁^{-1/3}) rounds. We then prove this analysis close to tight with an almost-matching lower bound. To better understand the impact of smoothing on information spreading, we next turn our attention to static networks, proving a tight bound of Õ(k√n) rounds to solve k-message broadcast, which is better than what our strategy can achieve in the dynamic setting. This confirms the intuition that although smoothed analysis reduces the difficulties induced by changing graph structures, it does not eliminate them altogether. Finally, we apply tools developed to support our smoothed analysis to prove an optimal result for k-message broadcast in so-called well-mixed networks in the absence of smoothing. By comparing this result to an existing lower bound for well-mixed networks, we establish a formal separation between oblivious and strongly adaptive adversaries with respect to well-mixed token spreading, partially resolving an open question on the impact of adversary strength on the k-message broadcast problem. 

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4. Singularly Optimal Randomized Leader Election

   https://doi.org/10.4230/LIPIcs.DISC.2020.22  

   Kutten, Shay; Moses Jr., William K.; Pandurangan, Gopal; Peleg, David (January 2020, 34th International Symposium on Distributed Computing (DISC 2020))

   null (Ed.)

   This paper concerns designing distributed algorithms that are singularly optimal, i.e., algorithms that are simultaneously time and message optimal, for the fundamental leader election problem in networks. Our main result is a randomized distributed leader election algorithm for asynchronous complete networks that is essentially (up to a polylogarithmic factor) singularly optimal. Our algorithm uses O(n) messages with high probability and runs in O(log² n) time (with high probability) to elect a unique leader. The O(n) message complexity should be contrasted with the Ω(n log n) lower bounds for the deterministic message complexity of leader election algorithms (regardless of time), proven by Korach, Moran, and Zaks (TCS, 1989) for asynchronous algorithms and by Afek and Gafni (SIAM J. Comput., 1991) for synchronous networks. Hence, our result also separates the message complexities of randomized and deterministic leader election. More importantly, our (randomized) time complexity of O(log² n) for obtaining the optimal O(n) message complexity is significantly smaller than the long-standing Θ̃(n) time complexity obtained by Afek and Gafni and by Singh (SIAM J. Comput., 1997) for message optimal (deterministic) election in asynchronous networks. Afek and Gafni also conjectured that Θ̃(n) time would be optimal for message-optimal asynchronous algorithms. Our result shows that randomized algorithms are significantly faster. Turning to synchronous complete networks, Afek and Gafni showed an essentially singularly optimal deterministic algorithm with O(log n) time and O(n log n) messages. Ramanathan et al. (Distrib. Comput. 2007) used randomization to improve the message complexity, and showed a randomized algorithm with O(n) messages but still with O(log n) time (with failure probability O(1 / log^{Ω(1)}n)). Our second result shows that synchronous complete networks admit a tightly singularly optimal randomized algorithm, with O(1) time and O(n) messages (both bounds are optimal). Moreover, our algorithm’s time bound holds with certainty, and its message bound holds with high probability, i.e., 1-1/n^c for constant c. Our results demonstrate that leader election can be solved in a simultaneously message and time-efficient manner in asynchronous complete networks using randomization. It is open whether this is possible in asynchronous general networks. 

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5. Sleeping is Efficient: MIS in O(1)-rounds Node-averaged Awake Complexity

   https://doi.org/10.1145/3382734.3405718  

   Chatterjee, Soumyottam; Gmyr, Robert; Pandurangan, Gopal (July 2020, PODC '20: Proceedings of the 39th Symposium on Principles of Distributed Computing)

   null (Ed.)

   Maximal Independent Set (MIS) is one of the fundamental problems in distributed computing. The round (time) complexity of distributed MIS has traditionally focused on the worst-case time for all nodes to finish. The best-known (randomized) MIS algorithms take O(log n) worst-case rounds on general graphs (where n is the number of nodes). Breaking the O(log n) worst-case bound has been a longstanding open problem, while currently the best-known lower bound is [EQUATION] rounds. Motivated by the goal to reduce total energy consumption in energy-constrained networks such as sensor and ad hoc wireless networks, we take an alternative approach to measuring performance. We focus on minimizing the total (or equivalently, the average) time for all nodes to finish. It is not clear whether the currently best-known algorithms yield constant-round (or even o(log n)) node-averaged round complexity for MIS in general graphs. We posit the sleeping model, a generalization of the traditional model, that allows nodes to enter either "sleep" or "waking" states at any round. While waking state corresponds to the default state in the traditional model, in sleeping state a node is "offline", i.e., it does not send or receive messages (and messages sent to it are dropped as well) and does not incur any time, communication, or local computation cost. Hence, in this model, only rounds in which a node is awake are counted and we are interested in minimizing the average as well as the worst-case number of rounds a node spends in the awake state, besides the traditional worst-case round complexity (i.e., the rounds for all nodes to finish including both the awake and sleeping rounds). Our main result is that we show that MIS can be solved in (expected) O(1) rounds under node-averaged awake complexity measure in the sleeping model. In particular, we present a randomized distributed algorithm for MIS that has expected O(1)-rounds node-averaged awake complexity and, with high probability1 has O(log n)-rounds worst-case awake complexity and O(log3.41 n)-rounds worst-case complexity. Our work is a step towards understanding the node-averaged complexity of MIS both in the traditional and sleeping models, as well as designing energy-efficient distributed algorithms for energy-constrained networks. 

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