26 research outputs found
The Computational Power of Beeps
In this paper, we study the quantity of computational resources (state
machine states and/or probabilistic transition precision) needed to solve
specific problems in a single hop network where nodes communicate using only
beeps. We begin by focusing on randomized leader election. We prove a lower
bound on the states required to solve this problem with a given error bound,
probability precision, and (when relevant) network size lower bound. We then
show the bound tight with a matching upper bound. Noting that our optimal upper
bound is slow, we describe two faster algorithms that trade some state
optimality to gain efficiency. We then turn our attention to more general
classes of problems by proving that once you have enough states to solve leader
election with a given error bound, you have (within constant factors) enough
states to simulate correctly, with this same error bound, a logspace TM with a
constant number of unary input tapes: allowing you to solve a large and
expressive set of problems. These results identify a key simplicity threshold
beyond which useful distributed computation is possible in the beeping model.Comment: Extended abstract to appear in the Proceedings of the International
Symposium on Distributed Computing (DISC 2015
Noisy Beeping Networks
We introduce noisy beeping networks, where nodes have limited communication
capabilities, namely, they can only emit energy or sense the channel for
energy. Furthermore, imperfections may cause devices to malfunction with some
fixed probability when sensing the channel, which amounts to deducing a noisy
received transmission. Such noisy networks have implications for
ultra-lightweight sensor networks and biological systems.
We show how to compute tasks in a noise-resilient manner over noisy beeping
networks of arbitrary structure. In particular, we transform any algorithm that
assumes a noiseless beeping network (of size ) into a noise-resilient
version while incurring a multiplicative overhead of only in its
round complexity, with high probability. We show that our coding is optimal for
some tasks, such as node-coloring of a clique.
We further show how to simulate a large family of algorithms designed for
distributed networks in the CONGEST() model over a noisy beeping network.
The simulation succeeds with high probability and incurs an asymptotic
multiplicative overhead of in the
round complexity, where is the maximal degree of the network. The
overhead is tight for certain graphs, e.g., a clique. Further, this simulation
implies a constant overhead coding for constant-degree networks
The Energy Complexity of Broadcast
Energy is often the most constrained resource in networks of battery-powered
devices, and as devices become smaller, they spend a larger fraction of their
energy on communication (transceiver usage) not computation. As an imperfect
proxy for true energy usage, we define energy complexity to be the number of
time slots a device transmits/listens; idle time and computation are free.
In this paper we investigate the energy complexity of fundamental
communication primitives such as broadcast in multi-hop radio networks. We
consider models with collision detection (CD) and without (No-CD), as well as
both randomized and deterministic algorithms. Some take-away messages from this
work include:
1. The energy complexity of broadcast in a multi-hop network is intimately
connected to the time complexity of leader election in a single-hop (clique)
network. Many existing lower bounds on time complexity immediately transfer to
energy complexity. For example, in the CD and No-CD models, we need
and energy, respectively.
2. The energy lower bounds above can almost be achieved, given sufficient
() time. In the CD and No-CD models we can solve broadcast using
energy and energy,
respectively.
3. The complexity measures of Energy and Time are in conflict, and it is an
open problem whether both can be minimized simultaneously. We give a tradeoff
showing it is possible to be nearly optimal in both measures simultaneously.
For any constant , broadcast can be solved in
time with
energy, where is the diameter of the network
Deterministic Digital Clustering of Wireless Ad Hoc Networks
We consider deterministic distributed communication in wireless ad hoc
networks of identical weak devices under the SINR model without predefined
infrastructure. Most algorithmic results in this model rely on various
additional features or capabilities, e.g., randomization, access to geographic
coordinates, power control, carrier sensing with various precision of
measurements, and/or interference cancellation. We study a pure scenario, when
no such properties are available. As a general tool, we develop a deterministic
distributed clustering algorithm. Our solution relies on a new type of
combinatorial structures (selectors), which might be of independent interest.
Using the clustering, we develop a deterministic distributed local broadcast
algorithm accomplishing this task in rounds, where
is the density of the network. To the best of our knowledge, this is
the first solution in pure scenario which is only polylog away from the
universal lower bound , valid also for scenarios with
randomization and other features. Therefore, none of these features
substantially helps in performing the local broadcast task. Using clustering,
we also build a deterministic global broadcast algorithm that terminates within
rounds, where is the diameter of the
network. This result is complemented by a lower bound , where is the path-loss parameter of the
environment. This lower bound shows that randomization or knowledge of own
location substantially help (by a factor polynomial in ) in the global
broadcast. Therefore, unlike in the case of local broadcast, some additional
model features may help in global broadcast
Radio network algorithms for global communication
Radio networks are a distributed computing model capturing the behavior of devices that communicate via wireless transmissions. Applications of wireless networks have expanded hugely in recent decades due to their convenience and versatility. However, wireless communication presents practical difficulties, particularly in avoiding interference between transmissions. The radio network model provides a theoretical distillation of the behavior of such networks, in order to better understand and facilitate communication.
This thesis concerns fundamental global communication tasks in the radio network model: that is, tasks that require relaying messages throughout the entire network. Examples include broadcasting a message to all devices in a network, or reaching agreement on a single device to act as a coordinator.
We present algorithms to perform global tasks efficiently, and show improved asymptotic running times over a range of environments and model variants. Our results demonstrate an advance over the state of the art in radio network research, and in many cases reach or approach known lower bounds
Weak models of wireless distributed computing Comparison between radio networks and population protocols
This thesis compares weak distributed computing models that are suit- able for extremely limited wireless networks. The comparison is mainly between multiple variations of radio networks and population protocols. The analysis is based on model features, computability and algorithmic complexity. The thesis analyses essential and optional model features, and organizes the models accordingly. It discusses the applicability of results from stronger models to radio network models, including impossibility results, algorithms and their runtime. It analyzes different radio network algorithms for the classical problems in terms of their features, and it discusses their applicability to other radio network models. It reviews the fundamental differences between population protocols and radio networks. Lastly, the comparative analysis summarizes fundamental differences and separating features
Probabilistic methods for distributed information dissemination
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2013.Cataloged from PDF version of thesis.Includes bibliographical references (p. 457-484).The ever-increasing growth of modern networks comes with a paradigm shift in network operation. Networks can no longer be abstracted as deterministic, centrally controlled systems with static topologies but need to be understood as highly distributed, dynamic systems with inherent unreliabilities. This makes many communication, coordination and computation tasks challenging and in many scenarios communication becomes a crucial bottleneck. In this thesis, we develop new algorithms and techniques to address these challenges. In particular we concentrate on broadcast and information dissemination tasks and introduce novel ideas on how randomization can lead to powerful, simple and practical communication primitives suitable for these modern networks. In this endeavor we combine and further develop tools from different disciplines trying to simultaneously addresses the distributed, information theoretic and algorithmic aspects of network communication. The two main probabilistic techniques developed to disseminate information in a network are gossip and random linear network coding. Gossip is an alternative to classical flooding approaches: Instead of nodes repeatedly forwarding information to all their neighbors, gossiping nodes forward information only to a small number of (random) neighbors. We show that, when done right, gossip disperses information almost as quickly as flooding, albeit with a drastically reduced communication overhead. Random linear network coding (RLNC) applies when a large amount of information or many messages are to be disseminated. Instead of routing messages through intermediate nodes, that is, following a classical store-and-forward approach, RLNC mixes messages together by forwarding random linear combinations of messages. The simplicity and topology-obliviousness of this approach makes RLNC particularly interesting for the distributed settings considered in this thesis. Unfortunately the performance of RLNC was not well understood even for the simplest such settings. We introduce a simple yet powerful analysis technique that allows us to prove optimal performance guarantees for all settings considered in the literature and many more that were not analyzable so far. Specifically, we give many new results for RLNC gossip algorithms, RLNC algorithms for dynamic networks, and RLNC with correlated data. We also provide a novel highly efficient distributed implementation of RLNC that achieves these performance guarantees while buffering only a minimal amount of information at intermediate nodes. We then apply our techniques to improve communication primitives in multi-hop radio networks. While radio networks inherently support broadcast communications, e.g., from one node to all surrounding nodes, interference of simultaneous transmissions makes multihop broadcast communication an interesting challenge. We show that, again, randomization holds the key for obtaining simple, efficient and distributed information dissemination protocols. In particular, using random back-off strategies to coordinate access to the shared medium leads to optimal gossip-like communications and applying RLNC achieves the first throughput-optimal multi-message communication primitives. Lastly we apply our probabilistic approach for analyzing simple, distributed propagation protocols in a broader context by studying algorithms for the Lovász Local Lemma. These algorithms find solutions to certain local constraint satisfaction problems by randomly fixing and propagating violations locally. Our two main results show that, firstly, there are also efficient deterministic propagation strategies achieving the same and, secondly, using the random fixing strategy has the advantage of producing not just an arbitrary solution but an approximately uniformly random one. Both results lead to simple, constructions for a many locally consistent structures of interest that were not known to be efficiently constructable before.by Bernhard Haeupler.Ph.D