14,798 research outputs found
Algorithms for Fast Aggregated Convergecast in Sensor Networks
Fast and periodic collection of aggregated data
is of considerable interest for mission-critical and continuous
monitoring applications in sensor networks. In the many-to-one
communication paradigm, referred to as convergecast, we focus
on applications wherein data packets are aggregated at each hop
en-route to the sink along a tree-based routing topology, and
address the problem of minimizing the convergecast schedule
length by utilizing multiple frequency channels. The primary
hindrance in minimizing the schedule length is the presence of
interfering links. We prove that it is NP-complete to determine
whether all the interfering links in an arbitrary network can
be removed using at most a constant number of frequencies.
We give a sufficient condition on the number of frequencies for
which all the interfering links can be removed, and propose a
polynomial time algorithm that minimizes the schedule length
in this case. We also prove that minimizing the schedule length
for a given number of frequencies on an arbitrary network is
NP-complete, and describe a greedy scheme that gives a constant
factor approximation on unit disk graphs. When the routing tree
is not given as an input to the problem, we prove that a constant
factor approximation is still achievable for degree-bounded trees.
Finally, we evaluate our algorithms through simulations and
compare their performance under different network parameters
Multi-Channel Scheduling for Fast Convergecast in Wireless Sensor Networks
We explore the following fundamental question -
how fast can information be collected from a wireless sensor
network? We consider a number of design parameters such
as, power control, time and frequency scheduling, and routing.
There are essentially two factors that hinder efficient data
collection - interference and the half-duplex single-transceiver
radios. We show that while power control helps in reducing the
number of transmission slots to complete a convergecast under a
single frequency channel, scheduling transmissions on different
frequency channels is more efficient in mitigating the effects of
interference (empirically, 6 channels suffice for most 100-node
networks). With these observations, we define a receiver-based
channel assignment problem, and prove it to be NP-complete on
general graphs. We then introduce a greedy channel assignment
algorithm that efficiently eliminates interference, and compare
its performance with other existing schemes via simulations.
Once the interference is completely eliminated, we show that
with half-duplex single-transceiver radios the achievable schedule
length is lower-bounded by max(2nk â 1,N), where nk is the
maximum number of nodes on any subtree and N is the number
of nodes in the network. We modify an existing distributed time
slot assignment algorithm to achieve this bound when a suitable
balanced routing scheme is employed. Through extensive simulations,
we demonstrate that convergecast can be completed within
up to 50% less time slots, in 100-node networks, using multiple
channels as compared to that with single-channel communication.
Finally, we also demonstrate further improvements that are
possible when the sink is equipped with multiple transceivers
or when there are multiple sinks to collect data
Optimal Collision/Conflict-free Distance-2 Coloring in Synchronous Broadcast/Receive Tree Networks
This article is on message-passing systems where communication is (a)
synchronous and (b) based on the "broadcast/receive" pair of communication
operations. "Synchronous" means that time is discrete and appears as a sequence
of time slots (or rounds) such that each message is received in the very same
round in which it is sent. "Broadcast/receive" means that during a round a
process can either broadcast a message to its neighbors or receive a message
from one of them. In such a communication model, no two neighbors of the same
process, nor a process and any of its neighbors, must be allowed to broadcast
during the same time slot (thereby preventing message collisions in the first
case, and message conflicts in the second case). From a graph theory point of
view, the allocation of slots to processes is know as the distance-2 coloring
problem: a color must be associated with each process (defining the time slots
in which it will be allowed to broadcast) in such a way that any two processes
at distance at most 2 obtain different colors, while the total number of colors
is "as small as possible". The paper presents a parallel message-passing
distance-2 coloring algorithm suited to trees, whose roots are dynamically
defined. This algorithm, which is itself collision-free and conflict-free, uses
colors where is the maximal degree of the graph (hence
the algorithm is color-optimal). It does not require all processes to have
different initial identities, and its time complexity is , where d
is the depth of the tree. As far as we know, this is the first distributed
distance-2 coloring algorithm designed for the broadcast/receive round-based
communication model, which owns all the previous properties.Comment: 19 pages including one appendix. One Figur
On the Distributed Complexity of Large-Scale Graph Computations
Motivated by the increasing need to understand the distributed algorithmic
foundations of large-scale graph computations, we study some fundamental graph
problems in a message-passing model for distributed computing where
machines jointly perform computations on graphs with nodes (typically, ). The input graph is assumed to be initially randomly partitioned among
the machines, a common implementation in many real-world systems.
Communication is point-to-point, and the goal is to minimize the number of
communication {\em rounds} of the computation.
Our main contribution is the {\em General Lower Bound Theorem}, a theorem
that can be used to show non-trivial lower bounds on the round complexity of
distributed large-scale data computations. The General Lower Bound Theorem is
established via an information-theoretic approach that relates the round
complexity to the minimal amount of information required by machines to solve
the problem. Our approach is generic and this theorem can be used in a
"cookbook" fashion to show distributed lower bounds in the context of several
problems, including non-graph problems. We present two applications by showing
(almost) tight lower bounds for the round complexity of two fundamental graph
problems, namely {\em PageRank computation} and {\em triangle enumeration}. Our
approach, as demonstrated in the case of PageRank, can yield tight lower bounds
for problems (including, and especially, under a stochastic partition of the
input) where communication complexity techniques are not obvious.
Our approach, as demonstrated in the case of triangle enumeration, can yield
stronger round lower bounds as well as message-round tradeoffs compared to
approaches that use communication complexity techniques
Empathic Neural Responses Predict Group Allegiance.
Watching another person in pain activates brain areas involved in the sensation of our own pain. Importantly, this neural mirroring is not constant; rather, it is modulated by our beliefs about their intentions, circumstances, and group allegiances. We investigated if the neural empathic response is modulated by minimally-differentiating information (e.g., a simple text label indicating another's religious belief), and if neural activity changes predict ingroups and outgroups across independent paradigms. We found that the empathic response was larger when participants viewed a painful event occurring to a hand labeled with their own religion (ingroup) than to a hand labeled with a different religion (outgroup). Counterintuitively, the magnitude of this bias correlated positively with the magnitude of participants' self-reported empathy. A multivariate classifier, using mean activity in empathy-related brain regions as features, discriminated ingroup from outgroup with 72% accuracy; the classifier's confidence correlated with belief certainty. This classifier generalized successfully to validation experiments in which the ingroup condition was based on an arbitrary group assignment. Empathy networks thus allow for the classification of long-held, newly-modified and arbitrarily-formed ingroups and outgroups. This is the first report of a single machine learning model on neural activation that generalizes to multiple representations of ingroup and outgroup. The current findings may prove useful as an objective diagnostic tool to measure the magnitude of one's group affiliations, and the effectiveness of interventions to reduce ingroup biases
Graph cluster randomization: network exposure to multiple universes
A/B testing is a standard approach for evaluating the effect of online
experiments; the goal is to estimate the `average treatment effect' of a new
feature or condition by exposing a sample of the overall population to it. A
drawback with A/B testing is that it is poorly suited for experiments involving
social interference, when the treatment of individuals spills over to
neighboring individuals along an underlying social network. In this work, we
propose a novel methodology using graph clustering to analyze average treatment
effects under social interference. To begin, we characterize graph-theoretic
conditions under which individuals can be considered to be `network exposed' to
an experiment. We then show how graph cluster randomization admits an efficient
exact algorithm to compute the probabilities for each vertex being network
exposed under several of these exposure conditions. Using these probabilities
as inverse weights, a Horvitz-Thompson estimator can then provide an effect
estimate that is unbiased, provided that the exposure model has been properly
specified.
Given an estimator that is unbiased, we focus on minimizing the variance.
First, we develop simple sufficient conditions for the variance of the
estimator to be asymptotically small in n, the size of the graph. However, for
general randomization schemes, this variance can be lower bounded by an
exponential function of the degrees of a graph. In contrast, we show that if a
graph satisfies a restricted-growth condition on the growth rate of
neighborhoods, then there exists a natural clustering algorithm, based on
vertex neighborhoods, for which the variance of the estimator can be upper
bounded by a linear function of the degrees. Thus we show that proper cluster
randomization can lead to exponentially lower estimator variance when
experimentally measuring average treatment effects under interference.Comment: 9 pages, 2 figure
Topological and Graph-coloring Conditions on the Parameter-independent Stability of Second-order Networked Systems
In this paper, we study parameter-independent stability in qualitatively
heterogeneous passive networked systems containing damped and undamped nodes.
Given the graph topology and a set of damped nodes, we ask if output consensus
is achieved for all system parameter values. For given parameter values, an
eigenspace analysis is used to determine output consensus. The extension to
parameter-independent stability is characterized by a coloring problem, named
the richly balanced coloring (RBC) problem. The RBC problem asks if all nodes
of the graph can be colored red, blue and black in such a way that (i) every
damped node is black, (ii) every black node has blue neighbors if and only if
it has red neighbors, and (iii) not all nodes in the graph are black. Such a
colored graph is referred to as a richly balanced colored graph.
Parameter-independent stability is guaranteed if there does not exist a richly
balanced coloring. The RBC problem is shown to cover another well-known graph
coloring scheme known as zero forcing sets. That is, if the damped nodes form a
zero forcing set in the graph, then a richly balanced coloring does not exist
and thus, parameter-independent stability is guaranteed. However, the full
equivalence of zero forcing sets and parameter-independent stability holds only
true for tree graphs. For more general graphs with few fundamental cycles an
algorithm, named chord node coloring, is proposed that significantly
outperforms a brute-force search for solving the NP-complete RBC problem.Comment: 30 pages, accepted for publication in SICO
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