1,013 research outputs found
Polynomial-Time Space-Optimal Silent Self-Stabilizing Minimum-Degree Spanning Tree Construction
Motivated by applications to sensor networks, as well as to many other areas,
this paper studies the construction of minimum-degree spanning trees. We
consider the classical node-register state model, with a weakly fair scheduler,
and we present a space-optimal \emph{silent} self-stabilizing construction of
minimum-degree spanning trees in this model. Computing a spanning tree with
minimum degree is NP-hard. Therefore, we actually focus on constructing a
spanning tree whose degree is within one from the optimal. Our algorithm uses
registers on bits, converges in a polynomial number of rounds, and
performs polynomial-time computation at each node. Specifically, the algorithm
constructs and stabilizes on a special class of spanning trees, with degree at
most . Indeed, we prove that, unless NP coNP, there are no
proof-labeling schemes involving polynomial-time computation at each node for
the whole family of spanning trees with degree at most . Up to our
knowledge, this is the first example of the design of a compact silent
self-stabilizing algorithm constructing, and stabilizing on a subset of optimal
solutions to a natural problem for which there are no time-efficient
proof-labeling schemes. On our way to design our algorithm, we establish a set
of independent results that may have interest on their own. In particular, we
describe a new space-optimal silent self-stabilizing spanning tree
construction, stabilizing on \emph{any} spanning tree, in rounds, and
using just \emph{one} additional bit compared to the size of the labels used to
certify trees. We also design a silent loop-free self-stabilizing algorithm for
transforming a tree into another tree. Last but not least, we provide a silent
self-stabilizing algorithm for computing and certifying the labels of a
NCA-labeling scheme
Silent MST approximation for tiny memory
In network distributed computing, minimum spanning tree (MST) is one of the
key problems, and silent self-stabilization one of the most demanding
fault-tolerance properties. For this problem and this model, a polynomial-time
algorithm with memory is known for the state model. This is
memory optimal for weights in the classic range (where
is the size of the network). In this paper, we go below this
memory, using approximation and parametrized complexity.
More specifically, our contributions are two-fold. We introduce a second
parameter~, which is the space needed to encode a weight, and we design a
silent polynomial-time self-stabilizing algorithm, with space . In turn, this allows us to get an approximation algorithm for the problem,
with a trade-off between the approximation ratio of the solution and the space
used. For polynomial weights, this trade-off goes smoothly from memory for an -approximation, to memory for exact solutions,
with for example memory for a 2-approximation
Memory lower bounds for deterministic self-stabilization
In the context of self-stabilization, a \emph{silent} algorithm guarantees
that the register of every node does not change once the algorithm has
stabilized. At the end of the 90's, Dolev et al. [Acta Inf. '99] showed that,
for finding the centers of a graph, for electing a leader, or for constructing
a spanning tree, every silent algorithm must use a memory of
bits per register in -node networks. Similarly, Korman et al. [Dist. Comp.
'07] proved, using the notion of proof-labeling-scheme, that, for constructing
a minimum-weight spanning trees (MST), every silent algorithm must use a memory
of bits per register. It follows that requiring the algorithm
to be silent has a cost in terms of memory space, while, in the context of
self-stabilization, where every node constantly checks the states of its
neighbors, the silence property can be of limited practical interest. In fact,
it is known that relaxing this requirement results in algorithms with smaller
space-complexity.
In this paper, we are aiming at measuring how much gain in terms of memory
can be expected by using arbitrary self-stabilizing algorithms, not necessarily
silent. To our knowledge, the only known lower bound on the memory requirement
for general algorithms, also established at the end of the 90's, is due to
Beauquier et al.~[PODC '99] who proved that registers of constant size are not
sufficient for leader election algorithms. We improve this result by
establishing a tight lower bound of bits per
register for self-stabilizing algorithms solving -coloring or
constructing a spanning tree in networks of maximum degree~. The lower
bound bits per register also holds for leader election
Schéma général auto-stabilisant et silencieux de constructions de type arbres couvrants
International audienceNous proposons un schéma général, appelé Scheme, qui calcule des structures de données de type arbres couvrants dans des réseaux quelconques. Scheme est auto-stabilisant, silencieux et malgré sa généralité, est aussi efficace. Il est écrit dans le modèle à mémoires localement partagées avec atomicité composite, et supposeun démon distribué inéquitable, l'hypothèse la plus faible concernant l'ordonnancement dans ce modèle. Son temps de stabilisation est d'au plus 4 nmax rondes, où nmax est le nombre maximum de processus dans une composante connexe. Nous montrons également des bornes supérieures polynomiales sur le temps de stabilisation en nombre de pas et de mouvements pour de grandes classes d'instances de l'algorithme Scheme. Nous illustrons la souplesse de notre approche en décrivant de telles instances résolvant des problèmes classiques tels que l'élection de leader et la construction d'arbres couvrants
Introduction to local certification
A distributed graph algorithm is basically an algorithm where every node of a
graph can look at its neighborhood at some distance in the graph and chose its
output. As distributed environment are subject to faults, an important issue is
to be able to check that the output is correct, or in general that the network
is in proper configuration with respect to some predicate. One would like this
checking to be very local, to avoid using too much resources. Unfortunately
most predicates cannot be checked this way, and that is where certification
comes into play. Local certification (also known as proof-labeling schemes,
locally checkable proofs or distributed verification) consists in assigning
labels to the nodes, that certify that the configuration is correct. There are
several point of view on this topic: it can be seen as a part of
self-stabilizing algorithms, as labeling problem, or as a non-deterministic
distributed decision.
This paper is an introduction to the domain of local certification, giving an
overview of the history, the techniques and the current research directions.Comment: Last update: minor editin
Disconnected components detection and rooted shortest-path tree maintenance in networks
International audienceMany articles deal with the problem of maintaining a rooted shortest-path tree. However, after some edge deletions, some nodes can be disconnected from the connected component of some distinguished node . In this case, an additional objective is to ensure the detection of the disconnection by the nodes that no longer belong to . We present a detailed analysis of a silent self-stabilizing algorithm. We prove that it solves this more demanding task in anonymous weighted networks with the following additional strong properties: it runs without any knowledge on the network and under the \emph{unfair} daemon, that is without any assumption on the asynchronous model. Moreover, it terminates in less than rounds for a network of nodes and hop-diameter
Making local algorithms efficiently self-stabilizing in arbitrary asynchronous environments
This paper deals with the trade-off between time, workload, and versatility
in self-stabilization, a general and lightweight fault-tolerant concept in
distributed computing.In this context, we propose a transformer that provides
an asynchronous silent self-stabilizing version Trans(AlgI) of any terminating
synchronous algorithm AlgI. The transformed algorithm Trans(AlgI) works under
the distributed unfair daemon and is efficient both in moves and rounds.Our
transformer allows to easily obtain fully-polynomial silent self-stabilizing
solutions that are also asymptotically optimal in rounds.We illustrate the
efficiency and versatility of our transformer with several efficient (i.e.,
fully-polynomial) silent self-stabilizing instances solving major distributed
computing problems, namely vertex coloring, Breadth-First Search (BFS) spanning
tree construction, k-clustering, and leader election
Self-stabilizing k-clustering in mobile ad hoc networks
In this thesis, two silent self-stabilizing asynchronous distributed algorithms are given for constructing a k-clustering of a connected network of processes. These are the first self-stabilizing solutions to this problem. One algorithm, FLOOD, takes O( k) time and uses O(k log n) space per process, while the second algorithm, BFS-MIS-CLSTR, takes O(n) time and uses O(log n) space; where n is the size of the network. Processes have unique IDs, and there is no designated leader. BFS-MIS-CLSTR solves three problems; it elects a leader and constructs a BFS tree for the network, constructs a minimal independent set, and finally a k-clustering. Finding a minimal k-clustering is known to be NP -hard. If the network is a unit disk graph in a plane, BFS-MIS-CLSTR is within a factor of O(7.2552k) of choosing the minimal number of clusters; A lower bound is given, showing that any comparison-based algorithm for the k-clustering problem that takes o( diam) rounds has very bad worst case performance; Keywords: BFS tree construction, K-clustering, leader election, MIS construction, self-stabilization, unit disk graph
Trade-off between Time, Space, and Workload: the case of the Self-stabilizing Unison
We present a self-stabilizing algorithm for the (asynchronous) unison problem
which achieves an efficient trade-off between time, workload, and space in a
weak model. Precisely, our algorithm is defined in the atomic-state model and
works in anonymous networks in which even local ports are unlabeled. It makes
no assumption on the daemon and thus stabilizes under the weakest one: the
distributed unfair daemon.
In a -node network of diameter and assuming a period ,
our algorithm only requires bits per node to achieve full
polynomiality as it stabilizes in at most rounds and moves. In particular and to the best of our knowledge, it is the first
self-stabilizing unison for arbitrary anonymous networks achieving an
asymptotically optimal stabilization time in rounds using a bounded memory at
each node.
Finally, we show that our solution allows to efficiently simulate synchronous
self-stabilizing algorithms in an asynchronous environment. This provides a new
state-of-the-art algorithm solving both the leader election and the spanning
tree construction problem in any identified connected network which, to the
best of our knowledge, beat all existing solutions of the literature.Comment: arXiv admin note: substantial text overlap with arXiv:2307.0663
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