4,370 research outputs found
Time-Varying Graphs and Dynamic Networks
The past few years have seen intensive research efforts carried out in some
apparently unrelated areas of dynamic systems -- delay-tolerant networks,
opportunistic-mobility networks, social networks -- obtaining closely related
insights. Indeed, the concepts discovered in these investigations can be viewed
as parts of the same conceptual universe; and the formal models proposed so far
to express some specific concepts are components of a larger formal description
of this universe. The main contribution of this paper is to integrate the vast
collection of concepts, formalisms, and results found in the literature into a
unified framework, which we call TVG (for time-varying graphs). Using this
framework, it is possible to express directly in the same formalism not only
the concepts common to all those different areas, but also those specific to
each. Based on this definitional work, employing both existing results and
original observations, we present a hierarchical classification of TVGs; each
class corresponds to a significant property examined in the distributed
computing literature. We then examine how TVGs can be used to study the
evolution of network properties, and propose different techniques, depending on
whether the indicators for these properties are a-temporal (as in the majority
of existing studies) or temporal. Finally, we briefly discuss the introduction
of randomness in TVGs.Comment: A short version appeared in ADHOC-NOW'11. This version is to be
published in Internation Journal of Parallel, Emergent and Distributed
System
Communication in networks with random dependent faults
The aim of this paper is to study communication in networks where nodes fail in a random dependent way. In order to capture fault dependencies, we introduce the neighborhood fault model, where damaging events, called spots, occur randomly and independently with probability p at nodes of a network, and cause faults in the given node and all of its neighbors. Faults at distance at most 2 become dependent in this model and are positively correlated. We investigate the impact of spot probability on feasibility and time of communication in the fault-free part of the network. We show a network which supports fast communication with high probability, if p ≤ 1/c log n. We also show that communication is not feasible with high probability in most classes of networks, for constant spot probabilities. For smaller spot probabilities, high probability communication is supported even by bounded degree networks. It is shown that the torus supports communication with high probability when p decreases faster than 1/n 1/2, and does not when p ∈ 1/O(n 1/2). Furthermore, a network built of tori is designed, with the same fault-tolerance properties and additionally supporting fast communication. We show, however, that networks of degree bounded by a constant d do not support communication with high probability, if p ∈ 1/O(n 1/d). While communication in networks with independent faults was widely studied, this is the first analytic paper which investigates network communication for random dependent faults. Keywords: Fault-tolerance, dependent faults, communication, crash faults, network connectivity
From invasion percolation to flow in rock fracture networks
The main purpose of this work is to simulate two-phase flow in the form of
immiscible displacement through anisotropic, three-dimensional (3D) discrete
fracture networks (DFN). The considered DFNs are artificially generated, based
on a general distribution function or are conditioned on measured data from
deep geological investigations. We introduce several modifications to the
invasion percolation (MIP) to incorporate fracture inclinations, intersection
lines, as well as the hydraulic path length inside the fractures. Additionally
a trapping algorithm is implemented that forbids any advance of the invading
fluid into a region, where the defending fluid is completely encircled by the
invader and has no escape route. We study invasion, saturation, and flow
through artificial fracture networks, with varying anisotropy and size and
finally compare our findings to well studied, conditioned fracture networks.Comment: 18 pages, 10 figure
Bicomponents and the robustness of networks to failure
A common definition of a robust connection between two nodes in a network
such as a communication network is that there should be at least two
independent paths connecting them, so that the failure of no single node in the
network causes them to become disconnected. This definition leads us naturally
to consider bicomponents, subnetworks in which every node has a robust
connection of this kind to every other. Here we study bicomponents in both real
and model networks using a combination of exact analytic techniques and
numerical methods. We show that standard network models predict there to be
essentially no small bicomponents in most networks, but there may be a giant
bicomponent, whose presence coincides with the presence of the ordinary giant
component, and we find that real networks seem by and large to follow this
pattern, although there are some interesting exceptions. We study the size of
the giant bicomponent as nodes in the network fail, using a specially developed
computer algorithm based on data trees, and find in some cases that our
networks are quite robust to failure, with large bicomponents persisting until
almost all vertices have been removed.Comment: 5 pages, 1 figure, 1 tabl
On Byzantine Broadcast in Loosely Connected Networks
We consider the problem of reliably broadcasting information in a multihop
asynchronous network that is subject to Byzantine failures. Most existing
approaches give conditions for perfect reliable broadcast (all correct nodes
deliver the authentic message and nothing else), but they require a highly
connected network. An approach giving only probabilistic guarantees (correct
nodes deliver the authentic message with high probability) was recently
proposed for loosely connected networks, such as grids and tori. Yet, the
proposed solution requires a specific initialization (that includes global
knowledge) of each node, which may be difficult or impossible to guarantee in
self-organizing networks - for instance, a wireless sensor network, especially
if they are prone to Byzantine failures. In this paper, we propose a new
protocol offering guarantees for loosely connected networks that does not
require such global knowledge dependent initialization. In more details, we
give a methodology to determine whether a set of nodes will always deliver the
authentic message, in any execution. Then, we give conditions for perfect
reliable broadcast in a torus network. Finally, we provide experimental
evaluation for our solution, and determine the number of randomly distributed
Byzantine failures than can be tolerated, for a given correct broadcast
probability.Comment: 1
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