40,514 research outputs found
A Message Passing Strategy for Decentralized Connectivity Maintenance in Agent Removal
In a multi-agent system, agents coordinate to achieve global tasks through
local communications. Coordination usually requires sufficient information
flow, which is usually depicted by the connectivity of the communication
network. In a networked system, removal of some agents may cause a
disconnection. In order to maintain connectivity in agent removal, one can
design a robust network topology that tolerates a finite number of agent
losses, and/or develop a control strategy that recovers connectivity. This
paper proposes a decentralized control scheme based on a sequence of
replacements, each of which occurs between an agent and one of its immediate
neighbors. The replacements always end with an agent, whose relocation does not
cause a disconnection. We show that such an agent can be reached by a local
rule utilizing only some local information available in agents' immediate
neighborhoods. As such, the proposed message passing strategy guarantees the
connectivity maintenance in arbitrary agent removal. Furthermore, we
significantly improve the optimality of the proposed scheme by incorporating
-criticality (i.e. the criticality of an agent in its
-neighborhood).Comment: 9 pages, 9 figure
On the complexity of color-avoiding site and bond percolation
The mathematical analysis of robustness and error-tolerance of complex
networks has been in the center of research interest. On the other hand, little
work has been done when the attack-tolerance of the vertices or edges are not
independent but certain classes of vertices or edges share a mutual
vulnerability. In this study, we consider a graph and we assign colors to the
vertices or edges, where the color-classes correspond to the shared
vulnerabilities. An important problem is to find robustly connected vertex
sets: nodes that remain connected to each other by paths providing any type of
error (i.e. erasing any vertices or edges of the given color). This is also
known as color-avoiding percolation. In this paper, we study various possible
modeling approaches of shared vulnerabilities, we analyze the computational
complexity of finding the robustly (color-avoiding) connected components. We
find that the presented approaches differ significantly regarding their
complexity.Comment: 14 page
Analysis of a Cone-Based Distributed Topology Control Algorithm for Wireless Multi-hop Networks
The topology of a wireless multi-hop network can be controlled by varying the
transmission power at each node. In this paper, we give a detailed analysis of
a cone-based distributed topology control algorithm. This algorithm, introduced
in [16], does not assume that nodes have GPS information available; rather it
depends only on directional information. Roughly speaking, the basic idea of
the algorithm is that a node transmits with the minimum power
required to ensure that in every cone of degree around
, there is some node that can reach with power . We show
that taking is a necessary and sufficient condition to
guarantee that network connectivity is preserved. More precisely, if there is a
path from to when every node communicates at maximum power, then, if
, there is still a path in the smallest symmetric graph
containing all edges such that can communicate with
using power . On the other hand, if ,
connectivity is not necessarily preserved. We also propose a set of
optimizations that further reduce power consumption and prove that they retain
network connectivity. Dynamic reconfiguration in the presence of failures and
mobility is also discussed. Simulation results are presented to demonstrate the
effectiveness of the algorithm and the optimizations.Comment: 10 page
Topology Control in Heterogeneous Wireless Networks: Problems and Solutions
Previous work on topology control usually assumes homogeneous wireless nodes with uniform transmission ranges. In this paper, we propose two localized topology control algorithms for heterogeneous wireless multi-hop networks with nonuniform transmission ranges: Directed Relative Neighborhood Graph (DRNG) and Directed Local Spanning Subgraph (DLSS). In both algorithms, each node selects a set of neighbors based on the locally collected information. We prove that (1) the topologies derived under DRNG and DLSS preserve the network connectivity; (2) the out degree of any node in the resulting topology by DLSS is bounded, while the out degree cannot be bounded in DRNG; and (3) the topologies generated by DRNG and DLSS preserve the network bi-directionality
Survivability in Time-varying Networks
Time-varying graphs are a useful model for networks with dynamic connectivity
such as vehicular networks, yet, despite their great modeling power, many
important features of time-varying graphs are still poorly understood. In this
paper, we study the survivability properties of time-varying networks against
unpredictable interruptions. We first show that the traditional definition of
survivability is not effective in time-varying networks, and propose a new
survivability framework. To evaluate the survivability of time-varying networks
under the new framework, we propose two metrics that are analogous to MaxFlow
and MinCut in static networks. We show that some fundamental
survivability-related results such as Menger's Theorem only conditionally hold
in time-varying networks. Then we analyze the complexity of computing the
proposed metrics and develop several approximation algorithms. Finally, we
conduct trace-driven simulations to demonstrate the application of our
survivability framework to the robust design of a real-world bus communication
network
2-Vertex Connectivity in Directed Graphs
We complement our study of 2-connectivity in directed graphs, by considering
the computation of the following 2-vertex-connectivity relations: We say that
two vertices v and w are 2-vertex-connected if there are two internally
vertex-disjoint paths from v to w and two internally vertex-disjoint paths from
w to v. We also say that v and w are vertex-resilient if the removal of any
vertex different from v and w leaves v and w in the same strongly connected
component. We show how to compute the above relations in linear time so that we
can report in constant time if two vertices are 2-vertex-connected or if they
are vertex-resilient. We also show how to compute in linear time a sparse
certificate for these relations, i.e., a subgraph of the input graph that has
O(n) edges and maintains the same 2-vertex-connectivity and vertex-resilience
relations as the input graph, where n is the number of vertices.Comment: arXiv admin note: substantial text overlap with arXiv:1407.304
Brain networks under attack : robustness properties and the impact of lesions
A growing number of studies approach the brain as a complex network, the so-called ‘connectome’. Adopting this framework, we examine what types or extent of damage the brain can withstand—referred to as network ‘robustness’—and conversely, which kind of distortions can be expected after brain lesions. To this end, we review computational lesion studies and empirical studies investigating network alterations in brain tumour, stroke and traumatic brain injury patients. Common to these three types of focal injury is that there is no unequivocal relationship between the anatomical lesion site and its topological characteristics within the brain network. Furthermore, large-scale network effects of these focal lesions are compared to those of a widely studied multifocal neurodegenerative disorder, Alzheimer’s disease, in which central parts of the connectome are preferentially affected. Results indicate that human brain networks are remarkably resilient to different types of lesions, compared to other types of complex networks such as random or scale-free networks. However, lesion effects have been found to depend critically on the topological position of the lesion. In particular, damage to network hub regions—and especially those connecting different subnetworks—was found to cause the largest disturbances in network organization. Regardless of lesion location, evidence from empirical and computational lesion studies shows that lesions cause significant alterations in global network topology. The direction of these changes though remains to be elucidated. Encouragingly, both empirical and modelling studies have indicated that after focal damage, the connectome carries the potential to recover at least to some extent, with normalization of graph metrics being related to improved behavioural and cognitive functioning. To conclude, we highlight possible clinical implications of these findings, point out several methodological limitations that pertain to the study of brain diseases adopting a network approach, and provide suggestions for future research
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