Communication complexity

About: Communication complexity is a research topic. Over the lifetime, 3870 publications have been published within this topic receiving 105832 citations.

Adaptive Distributed Outlier Detection for WSNs

Abstract: The paradigm of pervasive computing is gaining more and more attention nowadays, thanks to the possibility of obtaining precise and continuous monitoring. Ease of deployment and adaptivity are typically implemented by adopting autonomous and cooperative sensory devices; however, for such systems to be of any practical use, reliability and fault tolerance must be guaranteed, for instance by detecting corrupted readings amidst the huge amount of gathered sensory data. This paper proposes an adaptive distributed Bayesian approach for detecting outliers in data collected by a wireless sensor network; our algorithm aims at optimizing classification accuracy, time complexity and communication complexity, and also considering externally imposed constraints on such conflicting goals. The performed experimental evaluation showed that our approach is able to improve the considered metrics for latency and energy consumption, with limited impact on classification accuracy.

Fourier analysis for probabilistic communication complexity

Abstract: We use Fourier analysis to get general lower bounds for the probabilistic communication complexity of large classes of functions. We give some examples showing how to use our method in some known cases and for some new functions. Our main tool is an inequality by Kahn, Kalai, and Linial, derived from two lemmas of Beckner.

Fractional covers and communication complexity

Abstract: It is possible to view communication complexity as the solution of an integer programming problem. The authors relax this integer programming problem to a linear programming problem, and try to deduce from it information regarding the original communication complexity question. This approach works well for nondeterministic communication complexity. In this case the authors get a special case of Lovasz's fractional cover measure and use it to completely characterize the amortized nondeterministic communication complexity. In the case of deterministic complexity the situation is more complicated. The authors discuss two attempts, and obtain some results using each of them. >

Synchronous Byzantine Agreement with Expected O(1) Rounds, Expected O(n 2) Communication, and Optimal Resilience.

Abstract: We present new protocols for Byzantine agreement in the synchronous and authenticated setting, tolerating the optimal number of f faults among \(n=2f+1\) parties. Our protocols achieve an expected O(1) round complexity and an expected \(O(n^2)\) communication complexity. The exact round complexity in expectation is 10 for a static adversary and 16 for a strongly rushing adaptive adversary. For comparison, previous protocols in the same setting require expected 29 rounds.

The streaming complexity of cycle counting, sorting by reversals, and other problems

Abstract: In this paper we introduce a new technique for proving streaming lower bounds (and one-way communication lower bounds), by reductions from a problem called the Boolean Hidden Hypermatching problem (BHH). BHH is a generalization of the well-known Boolean Hidden Matching problem, which was used by Gavinsky et al. to prove an exponential separation between quantum communication complexity and one-way randomized communication complexity. We are the first to introduce BHH, and to prove a lower bound for it.The hardness of the BHH problem is inherently oneway: it is easy to solve BHH using logarithmic two-way communication, but it requires √n communication if Alice is only allowed to send messages to Bob, and not vice-versa. This one-wayness allows us to prove lower bounds, via reductions, for streaming problems and related communication problems whose hardness is also inherently one-way.By designing reductions from BHH, we prove lower bounds for the streaming complexity of approximating the sorting by reversal distance, of approximately counting the number of cycles in a 2-regular graph, and of other problems.For example, here is one lower bound that we prove, for a cycle-counting problem: Alice gets a perfect matching EA on a set of n nodes, and Bob gets a perfect matching EB on the same set of nodes. The union EA U EB is a collection of cycles, and the goal is to approximate the number of cycles in this collection. We prove that if Alice is allowed to send o(√n) bits to Bob (and Bob is not allowed to send anything to Alice), then the number of cycles cannot be approximated to within a factor of 1.999, even using a randomized protocol. We prove that it is not even possible to distinguish the case where all cycles are of length 4, from the case where all cycles are of length 8. This lower bound is "natively" one-way: With 4 rounds of communication, it is easy to distinguish these two cases.