Communication complexity

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

Joint distributed synchronization and positioning in UWB ad hoc networks using TOA

Abstract: In this paper, we describe a global distributed solution that enables the simultaneous performance of time synchronization and positioning in ultra-wideband (UWB) ad hoc networks. On the one hand, the proposed synchronization scheme basically relies on cooperative two-way-ranging/time-of-arrival transactions and a diffusion algorithm that ensures the convergence of clock parameters to average reference values in each node. Although the described solution is generic at first sight, its sensitivity to time-of-arrival accuracy imposes the choice of an impulse-radio ultra-wideband physical layer in the very context. On the other hand, a distributed algorithm coupled with this synchronization scheme mitigates the impact of non-line-of-sight ranging errors on positioning accuracy without any additional protocol hook. More particularly, the realistic UWB ranging error models we use take into account UWB channel effects, as well as detection noises and relative clock drifts. Then, it is demonstrated that a cooperative and distributed maximization of the log-likelihood of range estimates can reduce the uncertainty on estimated positions in comparison with classical distributed weighted least squares approaches. Finally, the proposed distributed maximum log-likelihood algorithm proves to preserve a reasonable level of complexity in each node by approximating asynchronously the positive gradient direction of the log-likelihood function. For both distributed synchronization and positioning algorithms, simulation results are provided to illustrate the relevance of such a solution.

Information Equals Amortized Communication

Abstract: We show how to efficiently simulate the sending of a message M to a receiver who has partial information about the message, so that the expected number of bits communicated in the simulation is close to the amount of additional information that the message reveals to the receiver. This is a generalization and strengthening of the Slepian-Wolf theorem, which shows how to carry out such a simulation with low amortized communication in the case that M is a deterministic function of X. A caveat is that our simulation is interactive. As a consequence, we prove that the internal information cost (namely the information revealed to the parties) involved in computing any relation or function using a two party interactive protocol is exactly equal to the amortized communication complexity of computing independent copies of the same relation or function. We also show that the only way to prove a strong direct sum theorem for randomized communication complexity is by solving a particular variant of the pointer jumping problem that we define. Our work implies that a strong direct sum theorem for communication complexity holds if and only if efficient compression of communication protocols is possible.

Minimizing charging delay in wireless rechargeable sensor networks

Abstract: As a pioneering experimental platform of wireless rechargeable sensor networks, the Wireless Identification and Sensing Platform (WISP) is an open-source platform that integrates sensing and computation capabilities to the traditional RFID tags. Different from traditional tags, a RFID-based wireless rechargeable sensor node needs to charge its onboard energy storage above a threshold in order to power its sensing, computation and communication components. Consequently, such charging delay imposes a unique design challenge for deploying wireless rechargeable sensor networks. In this paper, we tackle this problem by planning the optimal movement strategy of the RFID reader, such that the time to charge all nodes in the network above their energy threshold is minimized. We first propose an optimal solution using the linear programming method. To further reduce the computational complexity, we then introduce a heuristic solution with a provable approximation ratio of (1 + θ)/(1 - e) by discretizing the charging power on a two-dimensional space. Through extensive evaluations, we demonstrate that our design outperforms the set-cover-based design by an average of 24.7% while the computational complexity is O((N/e)2).

Algorithms for distributed functional monitoring

Abstract: We study what we call functional monitoring problems. We have k players each tracking their inputs, say player i tracking a multiset Ai(t) up until time t, and communicating with a central coordinator. The coordinator's task is to monitor a given function f computed over the union of the inputs ∪iAi(t), continuously at all times t. The goal is to minimize the number of bits communicated between the players and the coordinator. A simple example is when f is the sum, and the coordinator is required to alert when the sum of a distributed set of values exceeds a given threshold τ. Of interest is the approximate version where the coordinator outputs 1 if f ≥ τ and 0 if f ≤ (1 - e)τ. This defines the (k, f, τ, e) distributed, functional monitoring problem. Functional monitoring problems are fundamental in distributed systems, in particular sensor networks, where we must minimize communication; they also connect to problems in communication complexity, communication theory, and signal processing. Yet few formal bounds are known for functional monitoring. We give upper and lower bounds for the (k, f, τ, e) problem for some of the basic f's. In particular, we study frequency moments (F0, F1, F2). For F0 and F1, we obtain continuously monitoring algorithms with costs almost the same as their one-shot computation algorithms. However, for F2 the monitoring problem seems much harder. We give a carefully constructed multi-round algorithm that uses "sketch summaries" at multiple levels of detail and solves the (k, F2, τ, e) problem with communication O(k2/e+ (√k/e)3). Since frequency moment estimation is central to other problems, our results have immediate applications to histograms, wavelet computations, and others. Our algorithmic techniques are likely to be useful for other functional monitoring problems as well.

Adaptive Robust Distributed Learning in Diffusion Sensor Networks

Abstract: In this paper, the problem of adaptive distributed learning in diffusion networks is considered. The algorithms are developed within the convex set theoretic framework. More specifically, they are based on computationally simple geometric projections onto closed convex sets. The paper suggests a novel combine-project-adapt protocol for cooperation among the nodes of the network; such a protocol fits naturally with the philosophy that underlies the projection-based rationale. Moreover, the possibility that some of the nodes may fail is also considered and it is addressed by employing robust statistics loss functions. Such loss functions can easily be accommodated in the adopted algorithmic framework; all that is required from a loss function is convexity. Under some mild assumptions, the proposed algorithms enjoy monotonicity, asymptotic optimality, asymptotic consensus, strong convergence and linear complexity with respect to the number of unknown parameters. Finally, experiments in the context of the system-identification task verify the validity of the proposed algorithmic schemes, which are compared to other recent algorithms that have been developed for adaptive distributed learning.