41,412 research outputs found
Consensus Computation in Unreliable Networks: A System Theoretic Approach
This work addresses the problem of ensuring trustworthy computation in a
linear consensus network. A solution to this problem is relevant for several
tasks in multi-agent systems including motion coordination, clock
synchronization, and cooperative estimation. In a linear consensus network, we
allow for the presence of misbehaving agents, whose behavior deviate from the
nominal consensus evolution. We model misbehaviors as unknown and unmeasurable
inputs affecting the network, and we cast the misbehavior detection and
identification problem into an unknown-input system theoretic framework. We
consider two extreme cases of misbehaving agents, namely faulty (non-colluding)
and malicious (Byzantine) agents. First, we characterize the set of inputs that
allow misbehaving agents to affect the consensus network while remaining
undetected and/or unidentified from certain observing agents. Second, we
provide worst-case bounds for the number of concurrent faulty or malicious
agents that can be detected and identified. Precisely, the consensus network
needs to be 2k+1 (resp. k+1) connected for k malicious (resp. faulty) agents to
be generically detectable and identifiable by every well behaving agent. Third,
we quantify the effect of undetectable inputs on the final consensus value.
Fourth, we design three algorithms to detect and identify misbehaving agents.
The first and the second algorithm apply fault detection techniques, and
affords complete detection and identification if global knowledge of the
network is available to each agent, at a high computational cost. The third
algorithm is designed to exploit the presence in the network of weakly
interconnected subparts, and provides local detection and identification of
misbehaving agents whose behavior deviates more than a threshold, which is
quantified in terms of the interconnection structure
Robust Localization from Incomplete Local Information
We consider the problem of localizing wireless devices in an ad-hoc network
embedded in a d-dimensional Euclidean space. Obtaining a good estimation of
where wireless devices are located is crucial in wireless network applications
including environment monitoring, geographic routing and topology control. When
the positions of the devices are unknown and only local distance information is
given, we need to infer the positions from these local distance measurements.
This problem is particularly challenging when we only have access to
measurements that have limited accuracy and are incomplete. We consider the
extreme case of this limitation on the available information, namely only the
connectivity information is available, i.e., we only know whether a pair of
nodes is within a fixed detection range of each other or not, and no
information is known about how far apart they are. Further, to account for
detection failures, we assume that even if a pair of devices is within the
detection range, it fails to detect the presence of one another with some
probability and this probability of failure depends on how far apart those
devices are. Given this limited information, we investigate the performance of
a centralized positioning algorithm MDS-MAP introduced by Shang et al., and a
distributed positioning algorithm, introduced by Savarese et al., called
HOP-TERRAIN. In particular, for a network consisting of n devices positioned
randomly, we provide a bound on the resulting error for both algorithms. We
show that the error is bounded, decreasing at a rate that is proportional to
R/Rc, where Rc is the critical detection range when the resulting random
network starts to be connected, and R is the detection range of each device.Comment: 40 pages, 13 figure
Robustness and modular structure in networks
Complex networks have recently attracted much interest due to their
prevalence in nature and our daily lives [1, 2]. A critical property of a
network is its resilience to random breakdown and failure [3-6], typically
studied as a percolation problem [7-9] or by modeling cascading failures
[10-12]. Many complex systems, from power grids and the Internet to the brain
and society [13-15], can be modeled using modular networks comprised of small,
densely connected groups of nodes [16, 17]. These modules often overlap, with
network elements belonging to multiple modules [18, 19]. Yet existing work on
robustness has not considered the role of overlapping, modular structure. Here
we study the robustness of these systems to the failure of elements. We show
analytically and empirically that it is possible for the modules themselves to
become uncoupled or non-overlapping well before the network disintegrates. If
overlapping modular organization plays a role in overall functionality,
networks may be far more vulnerable than predicted by conventional percolation
theory.Comment: 14 pages, 9 figure
Randomized Initialization of a Wireless Multihop Network
Address autoconfiguration is an important mechanism required to set the IP
address of a node automatically in a wireless network. The address
autoconfiguration, also known as initialization or naming, consists to give a
unique identifier ranging from 1 to for a set of indistinguishable
nodes. We consider a wireless network where nodes (processors) are randomly
thrown in a square , uniformly and independently. We assume that the network
is synchronous and two nodes are able to communicate if they are within
distance at most of of each other ( is the transmitting/receiving
range). The model of this paper concerns nodes without the collision detection
ability: if two or more neighbors of a processor transmit concurrently at
the same time, then would not receive either messages. We suppose also that
nodes know neither the topology of the network nor the number of nodes in the
network. Moreover, they start indistinguishable, anonymous and unnamed. Under
this extremal scenario, we design and analyze a fully distributed protocol to
achieve the initialization task for a wireless multihop network of nodes
uniformly scattered in a square . We show how the transmitting range of the
deployed stations can affect the typical characteristics such as the degrees
and the diameter of the network. By allowing the nodes to transmit at a range
r= \sqrt{\frac{(1+\ell) \ln{n} \SIZE}{\pi n}} (slightly greater than the one
required to have a connected network), we show how to design a randomized
protocol running in expected time in order to assign a
unique number ranging from 1 to to each of the participating nodes
- âŠ