In their seminal PODC 1991 paper, Ostrovsky and Yung introduced the study of distributed computation in the presence of mobile adversaries which can dynamically appear throughout the network, analogous to a spread of ...
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ISBN:
(纸本)9798400701214
In their seminal PODC 1991 paper, Ostrovsky and Yung introduced the study of distributed computation in the presence of mobile adversaries which can dynamically appear throughout the network, analogous to a spread of a virus. Over the years, this setting has been studied mostly under the assumption that the communication graph is fully-connected. Resilient CONGEST algorithms for general graphs, on the other hand, are currently known only for the classical static setting, i.e., where the set of corrupted edges (or nodes) is fixed throughout the entire computation. We fill this missing gap by providing round-efficient simulations that translate given CONGEST algorithms into equivalent algorithms that are resilient against f-mobile edge adversaries, i.e., where the adversary controls a (possibly distinct) subset of f edges F-i in each round i. Our main results are: center dot Perfect-Security with Mobile Eavesdroppers. A translation of any r-round f-static-secure algorithm into an equivalent Theta(f)-mobile-secure algorithm with Theta(y) rounds. We also show that the f-static-secure algorithms of [Hitron, Parter and Yogev, DISC 2022 & ITCS 2023] can be modified into f-mobile-secure algorithms with the same number of rounds. center dot Resilience with Mobile Byzantine Adversaries. An f-mobile-byzantine simulation which is based on a decomposition of the graph into low-diameter edge-disjoint spanning trees. This provides us with near-optimal CONGEST compilers for expander graphs. It also leads to near-optimal compilers in the congested-clique model against Theta(n)-mobile adversaries. For general (2f + 1) edge-connected graphs with f-mobile adversary, we almost match the bounds known for the f-static setting, when provided a trusted pre-processing phase. Our results are based on a collection of tools borrowed from the area of interactive coding [Gelles, Found. Trends Theor. Comput. Sci. 2017], linear sketches and low-congestion graph decomposition. The introduced toolkit
We study the error resilience of the message exchange task: Two parties, each holding a private input, want to exchange their inputs. However, the channel connecting them is governed by an adversary that may corrupt a...
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ISBN:
(纸本)9781450380539
We study the error resilience of the message exchange task: Two parties, each holding a private input, want to exchange their inputs. However, the channel connecting them is governed by an adversary that may corrupt a constant fraction of the transmissions. What is the maximum fraction of corruptions that still allows the parties to exchange their inputs? For the non-adaptive channel, where the parties must agree in advance on the order in which they communicate, the maximum error resilience was shown to be 1/4 (see Braverman and Rao, STOC 2011). The problem was also studied over the adaptive channel, where the order in which the parties communicate may not be predetermined (Ghaffari, Haeupler, and Sudan, STOC 2014;Efremenko, Kol, and Saxena, STOC 2020). These works show that the adaptive channel admits much richer set of protocols but leave open the question of finding its maximum error resilience. In this work, we show that the maximum error resilience of a protocol for message exchange over the adaptive channel is 5/16, thereby settling the above question. Our result requires improving both the known upper bounds and the known lower bounds for the problem.
We consider the problem of implementing two-party interactive quantum communication over noisy channels, a necessary endeavor if we wish to fully reap quantum advantages for communication. For an arbitrary protocol wi...
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ISBN:
(纸本)9781450355599
We consider the problem of implementing two-party interactive quantum communication over noisy channels, a necessary endeavor if we wish to fully reap quantum advantages for communication. For an arbitrary protocol with n messages, designed for noiseless qudit channels (where d is arbitrary), our main result is a simulation method that fails with probability less than 2(-Theta(n epsilon)) and uses a qudit channel n (1 + Theta(root epsilon)) times, of which an epsilon fraction can be corrupted adversarially. The simulation is thus capacity achieving to leading order, and we conjecture that it is optimal up to a constant factor in the root epsilon term. Furthermore, the simulation is in a model that does not require pre-shared resources such as randomness or entanglement between the communicating parties. Perhaps surprisingly, this outperforms the best known overhead of 1 + O(root epsilon log log 1/epsilon) in the corresponding classical model, which is also conjectured to be optimal [Haeupler, FOCS' 14]. Our work also improves over the best previously known quantum result where the overhead is a non-explicit large constant [Brassard et al., FOCS' 14] for low..
We study the effect of noise on the n-party beeping model. In this model, in every round, each party may decide to either 'beep' or not. All parties hear a beep if and only if at least one party beeps. The bee...
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ISBN:
(纸本)9781450375825
We study the effect of noise on the n-party beeping model. In this model, in every round, each party may decide to either 'beep' or not. All parties hear a beep if and only if at least one party beeps. The beeping model is becoming increasingly popular, as it offers a very simple abstraction of wireless networks and is very well suited for studying biological phenomena. Still, the noise resilience of the beeping model is yet to be understood. Our main result is a lower bound, showing that making protocols in the beeping model resilient to noise may have a large performance overhead. Specifically, we give a protocol that works over the (noiseless) beeping model, and prove that any scheme that simulates this protocol over the beeping model with correlated stochastic noise will blow up the number of rounds by an O(logn) multiplicative factor. We complement this result by a matching upper bound, constructing a noise-resilient simulation scheme with O(logn) overhead for any noiseless beeping protocol.
interactive error correcting codes can protect interactive communication protocols against a constant fraction of adversarial errors, while incurring only a constant multiplicative overhead in the total communication....
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ISBN:
(纸本)9781450369794
interactive error correcting codes can protect interactive communication protocols against a constant fraction of adversarial errors, while incurring only a constant multiplicative overhead in the total communication. What is the maximum fraction of errors that such codes can protect against? For the non-adaptive channel, where the parties must agree in advance on the order in which they communicate, Braverman and Rao prove that the maximum error resilience is 1/4 (STOC, 2011). Ghaffari, Haeupler, and Sudan (STOC, 2014) consider the adaptive channel, where the order in which the parties communicate may not be fixed, and give a clever protocol that is resilient to a 2/7 fraction of errors. This was believed to be optimal. We revisit this result, and show how to overcome the 2/7 barrier. Specifically, we show that, over the adaptive channel, every twoparty communication protocol can be converted to a protocol that is resilient to 7/24 > 2/7 fraction of errors with only a constant multiplicative overhead to the total communication. The protocol is obtained by a novel implementation of a feedback mechanism over the adaptive channel.
A two-terminal interactive function computation problem with alternating messages is studied within the framework of distributed block source coding theory. For any finite number of messages, a single-letter character...
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A two-terminal interactive function computation problem with alternating messages is studied within the framework of distributed block source coding theory. For any finite number of messages, a single-letter characterization of the sum-rate-distortion function was established in previous works using standard information-theoretic techniques. This, however, does not provide a satisfactory characterization of the infinite-message limit, which is a new, unexplored dimension for asymptotic analysis in distributed block source coding involving potentially an infinite number of infinitesimal-rate messages. In this paper, the infinite-message sum-rate-distortion function, viewed as a functional of the joint source distribution and the distortion levels, is characterized as the least element of a partially ordered family of functionals having certain convex-geometric properties. The new characterization does not involve evaluating the infinite-message limit of a finite-message sum-rate-distortion expression. This characterization leads to a family of lower bounds for the infinite-message sum-rate-distortion expression and a simple criterion to test the optimality of any achievable infinite-message sum-rate-distortion expression. The new convex-geometric characterization is used to develop an iterative algorithm for evaluating any finite-message sum-rate-distortion function. It is also used to construct the first examples which demonstrate that for lossy source reproduction, two messages can strictly improve the one-message Wyner-Ziv rate-distortion function settling an unresolved question from a 1985 paper. It is shown that a single backward message of arbitrarily small rate can lead to an arbitrarily large gain in the sum-rate.
We consider the task of multiparty computation performed over networks in the presence of random noise. Given an n-party protocol that takes R rounds assuming noiseless communication, the goal is to find a coding sche...
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We consider the task of multiparty computation performed over networks in the presence of random noise. Given an n-party protocol that takes R rounds assuming noiseless communication, the goal is to find a coding scheme that takes R rounds and computes the same function with high probability even when the communication is noisy, while maintaining a constant asymptotic rate, i.e., while keeping lim infn, R.8 R/ R positive. Rajagopalan and Schulman (STOC'94) were the first to consider this question, and provided a coding scheme with rate O(1/ log(d + 1)), where d is the maximal degree in the network. While that scheme provides a constant rate coding for many practical situations, in the worst case, e.g., when the network is a complete graph, the rate is O(1/ log n), which tends to 0 as n tends to infinity. We revisit this question and provide an efficient coding scheme with a constant rate for the interesting case of fully connected networks. We furthermore extend the result and show that if a (d-regular) network has mixing time m, then there exists an efficient coding scheme with rate O(1/ m3 logm). This implies a constant rate coding scheme for any n-party protocol over a d-regular network with a constant mixing time, and in particular for random graphs with n vertices and degrees nO(1).
We consider the problem of making distributed computations robust to noise, in particular to worst-case (adversarial) corruptions of messages. We give a general distributed interactive coding scheme which simulates an...
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We consider the problem of making distributed computations robust to noise, in particular to worst-case (adversarial) corruptions of messages. We give a general distributed interactive coding scheme which simulates any asynchronous distributed protocol while tolerating an optimal corruption of a Theta(1/n) fraction of all messages and incurring a moderate blowup of O(nlog2n) in the communication complexity. Our result is the first fully distributed interactive coding scheme in which the topology of the communication network is not known in advance. Prior work required either a coordinating node to be connected to all other nodes in the network or assumed a synchronous network in which all nodes already know the complete topology of the network.
We consider the celebrated radio network model for abstracting communication in wireless networks. In this model, in any round, each node in the network may broadcast a message to all its neighbors. However, a node is...
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ISBN:
(纸本)9781728149523
We consider the celebrated radio network model for abstracting communication in wireless networks. In this model, in any round, each node in the network may broadcast a message to all its neighbors. However, a node is able to hear a message broadcast by a neighbor only if no collision occurred, meaning that it was the only neighbor broadcasting. While the (noiseless) radio network model received a lot of attention over the last few decades, the effect of noise on radio networks is still not well understood. In this paper, we take a step forward and show that making radio network protocols resilient to noise may require a substantial performance overhead. Specifically, we construct a multi -hop network and a communication protocol over this network that works in T rounds when there is no noise. We prove that any scheme that simulates our protocol and is resilient to stochastic noise, requires at least cT log(n) rounds, for some constant c. This stands in contrast to our previous result (STOC, 2018), showing that protocols over the single -hop (clique) network can be made noise resilient with only a constant overhead. Our result also settles a recent conjecture by Censor-Hillel, Haeupler, Hershkowitz, Zuzic (2018). We complement the above result by giving a scheme to simulate any protocol with a fixed order of transmissions with only an O(log (n)) overhead.
We consider fault-tolerant boolean formulas in which the output of a faulty gate is short-circuited to one of the gate's inputs. A recent result by Kalai et al. [FOCS 2012] converts any boolean formula into a resi...
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ISBN:
(纸本)9783959771160
We consider fault-tolerant boolean formulas in which the output of a faulty gate is short-circuited to one of the gate's inputs. A recent result by Kalai et al. [FOCS 2012] converts any boolean formula into a resilient formula of polynomial size that works correctly if less than a fraction 1/6 of the gates (on every input-to-output path) are faulty. We improve the result of Kalai et al., and show how to efficiently fortify any boolean formula against a fraction 1/5 of short-circuit gates per path, with only a polynomial blowup in size. We additionally show that it is impossible to obtain formulas with higher resilience and sub-exponential growth in size. Towards our results, we consider interactive coding schemes when noiseless feedback is present;these produce resilient boolean formulas via a Karchmer-Wigderson relation. We develop a coding scheme that resists up to a fraction 1/5 of corrupted transmissions in each direction of the interactive channel. We further show that such a level of noise is maximal for coding schemes with sub-exponential blowup in communication. Our coding scheme takes a surprising inspiration from Blockchain technology.
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