2,004 research outputs found
Self-stabilizing algorithms for Connected Vertex Cover and Clique decomposition problems
In many wireless networks, there is no fixed physical backbone nor
centralized network management. The nodes of such a network have to
self-organize in order to maintain a virtual backbone used to route messages.
Moreover, any node of the network can be a priori at the origin of a malicious
attack. Thus, in one hand the backbone must be fault-tolerant and in other hand
it can be useful to monitor all network communications to identify an attack as
soon as possible. We are interested in the minimum \emph{Connected Vertex
Cover} problem, a generalization of the classical minimum Vertex Cover problem,
which allows to obtain a connected backbone. Recently, Delbot et
al.~\cite{DelbotLP13} proposed a new centralized algorithm with a constant
approximation ratio of for this problem. In this paper, we propose a
distributed and self-stabilizing version of their algorithm with the same
approximation guarantee. To the best knowledge of the authors, it is the first
distributed and fault-tolerant algorithm for this problem. The approach
followed to solve the considered problem is based on the construction of a
connected minimal clique partition. Therefore, we also design the first
distributed self-stabilizing algorithm for this problem, which is of
independent interest
Universal Loop-Free Super-Stabilization
We propose an univesal scheme to design loop-free and super-stabilizing
protocols for constructing spanning trees optimizing any tree metrics (not only
those that are isomorphic to a shortest path tree). Our scheme combines a novel
super-stabilizing loop-free BFS with an existing self-stabilizing spanning tree
that optimizes a given metric. The composition result preserves the best
properties of both worlds: super-stabilization, loop-freedom, and optimization
of the original metric without any stabilization time penalty. As case study we
apply our composition mechanism to two well known metric-dependent spanning
trees: the maximum-flow tree and the minimum degree spanning tree
Algorithmes auto-stabilisants pour la construction de structures couvrantes réparties
This thesis deals with the self-stabilizing construction of spanning structures over a distributed system. Self-stabilization is a paradigm for fault-tolerance in distributed algorithms. It guarantees that the system eventually satisfies its specification after transient faults hit the system. Our model of distributed system assumes locally shared memories for communicating, unique identifiers for symmetry-breaking, and distributed daemon for execution scheduling, that is, the weakest proper daemon. More generally, we aim for the weakest possible assumptions, such as arbitrary topologies, in order to propose the most versatile constructions of distributed spanning structures. We present four original self-stabilizing algorithms achieving k-clustering, (f,g)-alliance construction, and ranking. For every of these problems, we prove the correctness of our solutions. Moreover, we analyze their time and space complexity using formal proofs and simulations. Finally, for the (f,g)-alliance problem, we consider the notion of safe convergence in addition to self-stabilization. It enforces the system to first quickly satisfy a specification that guarantees a minimum of conditions, and then to converge to a more stringent specification.Cette thèse s'intéresse à la construction auto-stabilisante de structures couvrantes dans un système réparti. L'auto-stabilisation est un paradigme pour la tolérance aux fautes dans les algorithmes répartis. Plus précisément, elle garantit que le système retrouve un comportement correct en temps fini après avoir été perturbé par des fautes transitoires. Notre modèle de système réparti se base sur des mémoires localement partagées pour la communication, des identifiants uniques pour briser les symétries et un ordonnanceur inéquitable, c'est-à-dire le plus faible des ordonnanceurs. Dans la mesure du possible, nous nous imposons d'utiliser les plus faibles hypothèses, afin d'obtenir les constructions les plus générales de structures couvrantes réparties. Nous présentons quatre algorithmes auto-stabilisants originaux pour le k-partitionnement, la construction d'une (f,g)-alliance et l'indexation. Pour chacun de ces problèmes, nous prouvons la correction de nos solutions. De plus, nous analysons leur complexité en temps et en espace à l'aide de preuves formelles et de simulations. Enfin, pour le problème de (f,g)-alliance, nous prenons en compte la notion de convergence sûre qui vient s'ajouter à celle d'auto-stabilisation. Elle garantit d'abord que le comportement du système assure rapidement un minimum de conditions, puis qu'il continue de converger jusqu'à se conformer à une spécification plus exigeante
On the Limits and Practice of Automatically Designing Self-Stabilization
A protocol is said to be self-stabilizing when the distributed system executing it is guaranteed to recover from any fault that does not cause permanent damage. Designing such protocols is hard since they must recover from all possible states, therefore we investigate how feasible it is to synthesize them automatically. We show that synthesizing stabilization on a fixed topology is NP-complete in the number of system states. When a solution is found, we further show that verifying its correctness on a general topology (with any number of processes) is undecidable, even for very simple unidirectional rings. Despite these negative results, we develop an algorithm to synthesize a self-stabilizing protocol given its desired topology, legitimate states, and behavior. By analogy to shadow puppetry, where a puppeteer may design a complex puppet to cast a desired shadow, a protocol may need to be designed in a complex way that does not even resemble its specification. Our shadow/puppet synthesis algorithm addresses this concern and, using a complete backtracking search, has automatically designed 4 new self-stabilizing protocols with minimal process space requirements: 2-state maximal matching on bidirectional rings, 5-state token passing on unidirectional rings, 3-state token passing on bidirectional chains, and 4-state orientation on daisy chains
Finding Optimal 2-Packing Sets on Arbitrary Graphs at Scale
A 2-packing set for an undirected graph is a subset such that any two vertices have no common
neighbors. Finding a 2-packing set of maximum cardinality is a NP-hard problem.
We develop a new approach to solve this problem on arbitrary graphs using its
close relation to the independent set problem. Thereby, our algorithm red2pack
uses new data reduction rules specific to the 2-packing set problem as well as
a graph transformation. Our experiments show that we outperform the
state-of-the-art for arbitrary graphs with respect to solution quality and also
are able to compute solutions multiple orders of magnitude faster than
previously possible. For example, we are able to solve 63% of our graphs to
optimality in less than a second while the competitor for arbitrary graphs can
only solve 5% of the graphs in the data set to optimality even with a 10 hour
time limit. Moreover, our approach can solve a wide range of large instances
that have previously been unsolved
Non-LTE models for synthetic spectra of type Ia supernovae. III. An accelerated lambda iteration procedure for the mutual interaction of strong spectral lines in SN Ia models with and without energy deposition
Context. Spectroscopic analyses to interpret the spectra of the brightest
supernovae from the UV to the near-IR provide a powerful tool with great
astrophysical potential for the determination of the physical state of the
ejecta, their chemical composition, and the SNe distances even at significant
redshifts.
Methods. We report on improvements of computing synthetic spectra for SNIa
with respect to i) an improved and sophisticated treatment of thousands of
strong lines that interact intricately with the "pseudo-continuum" formed
entirely by Doppler- shifted spectral lines, ii) an improved and expanded
atomic database, and iii) the inclusion of energy deposition within the ejecta.
Results. We show that an accelerated lambda iteration procedure we have
developed for the mutual interaction of strong spectral lines appearing in the
atmospheres of SNeIa solves the longstanding problem of transferring the
radiative energy from the UV into the optical regime. In detail we discuss
applications of the diagnostic technique by example of a standard SNIa, where
the comparison of calculated and observed spectra revealed that in the early
phases the consideration of the energy deposition within the spectrum-forming
regions of the ejecta does not qualitatively alter the shape of the spectra.
Conclusions. The results of our investigation lead to an improved
understanding of how the shape of the spectrum changes radically as function of
depth in the ejecta, and show how different emergent spectra are formed as a
result of the particular physical properties of SNe Ia ejecta and the resulting
peculiarities in the radiative transfer. This provides an important insight
into the process of extracting information from observed SNIa spectra, since
these spectra are a complex product of numerous unobservable SNIa spectral
features which are thus analyzed in parallel to the observable spectral
features.Comment: 27 pages, 19 figures. Submitted to A&A, revised versio
Distributed optimization algorithms for multihop wireless networks
Recent technological advances in low-cost computing and communication hardware design have led to the feasibility of large-scale deployments of wireless ad hoc and sensor networks. Due to their wireless and decentralized nature, multihop wireless networks are attractive for a variety of applications. However, these properties also pose significant challenges to their developers and therefore require new types of algorithms. In cases where traditional wired networks usually rely on some kind of centralized entity, in multihop wireless networks nodes have to cooperate in a distributed and self-organizing manner. Additional side constraints, such as energy consumption, have to be taken into account as well.
This thesis addresses practical problems from the domain of multihop wireless networks and investigates the application of mathematically justified distributed algorithms for solving them. Algorithms that are based on a mathematical model of an underlying optimization problem support a clear understanding of the assumptions and restrictions that are necessary in order to apply the algorithm to the problem at hand. Yet, the algorithms proposed in this thesis are simple enough to be formulated as a set of rules for each node to cooperate with other nodes in the network in computing optimal or approximate solutions. Nodes communicate with their neighbors by sending messages via wireless transmissions. Neither the size nor the number of messages grows rapidly with the size of the network.
The thesis represents a step towards a unified understanding of the application of distributed optimization algorithms to problems from the domain of multihop wireless networks. The problems considered serve as examples for related problems and demonstrate the design methodology of obtaining distributed algorithms from mathematical optimization methods
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