2,041 research outputs found
Bounds for self-stabilization in unidirectional networks
A distributed algorithm is self-stabilizing if after faults and attacks hit
the system and place it in some arbitrary global state, the systems recovers
from this catastrophic situation without external intervention in finite time.
Unidirectional networks preclude many common techniques in self-stabilization
from being used, such as preserving local predicates. In this paper, we
investigate the intrinsic complexity of achieving self-stabilization in
unidirectional networks, and focus on the classical vertex coloring problem.
When deterministic solutions are considered, we prove a lower bound of
states per process (where is the network size) and a recovery time of at
least actions in total. We present a deterministic algorithm with
matching upper bounds that performs in arbitrary graphs. When probabilistic
solutions are considered, we observe that at least states per
process and a recovery time of actions in total are required (where
denotes the maximal degree of the underlying simple undirected graph).
We present a probabilistically self-stabilizing algorithm that uses
states per process, where is a parameter of the
algorithm. When , the algorithm recovers in expected
actions. When may grow arbitrarily, the algorithm
recovers in expected O(n) actions in total. Thus, our algorithm can be made
optimal with respect to space or time complexity
Asynchronous neighborhood task synchronization
Faults are likely to occur in distributed systems. The motivation for designing self-stabilizing system is to be able to automatically recover from a faulty state. As per Dijkstra\u27s definition, a system is self-stabilizing if it converges to a desired state from an arbitrary state in a finite number of steps. The paradigm of self-stabilization is considered to be the most unified approach to designing fault-tolerant systems. Any type of faults, e.g., transient, process crashes and restart, link failures and recoveries, and byzantine faults, can be handled by a self-stabilizing system; Many applications in distributed systems involve multiple phases. Solving these applications require some degree of synchronization of phases. In this thesis research, we introduce a new problem, called asynchronous neighborhood task synchronization ( NTS ). In this problem, processes execute infinite instances of tasks, where a task consists of a set of steps. There are several requirements for this problem. Simultaneous execution of steps by the neighbors is allowed only if the steps are different. Every neighborhood is synchronized in the sense that all neighboring processes execute the same instance of a task. Although the NTS problem is applicable in nonfaulty environments, it is more challenging to solve this problem considering various types of faults. In this research, we will present a self-stabilizing solution to the NTS problem. The proposed solution is space optimal, fault containing, fully localized, and fully distributed. One of the most desirable properties of our algorithm is that it works under any (including unfair) daemon. We will discuss various applications of the NTS problem
Compact Deterministic Self-Stabilizing Leader Election: The Exponential Advantage of Being Talkative
This paper focuses on compact deterministic self-stabilizing solutions for
the leader election problem. When the protocol is required to be \emph{silent}
(i.e., when communication content remains fixed from some point in time during
any execution), there exists a lower bound of Omega(\log n) bits of memory per
node participating to the leader election (where n denotes the number of nodes
in the system). This lower bound holds even in rings. We present a new
deterministic (non-silent) self-stabilizing protocol for n-node rings that uses
only O(\log\log n) memory bits per node, and stabilizes in O(n\log^2 n) rounds.
Our protocol has several attractive features that make it suitable for
practical purposes. First, the communication model fits with the model used by
existing compilers for real networks. Second, the size of the ring (or any
upper bound on this size) needs not to be known by any node. Third, the node
identifiers can be of various sizes. Finally, no synchrony assumption, besides
a weakly fair scheduler, is assumed. Therefore, our result shows that, perhaps
surprisingly, trading silence for exponential improvement in term of memory
space does not come at a high cost regarding stabilization time or minimal
assumptions
Stabilizing Maximal Independent Set in Unidirectional Networks is Hard
A distributed algorithm is self-stabilizing if after faults and attacks hit
the system and place it in some arbitrary global state, the system recovers
from this catastrophic situation without external intervention in finite time.
In this paper, we consider the problem of constructing self-stabilizingly a
\emph{maximal independent set} in uniform unidirectional networks of arbitrary
shape. On the negative side, we present evidence that in uniform networks,
\emph{deterministic} self-stabilization of this problem is \emph{impossible}.
Also, the \emph{silence} property (\emph{i.e.} having communication fixed from
some point in every execution) is impossible to guarantee, either for
deterministic or for probabilistic variants of protocols. On the positive side,
we present a deterministic protocol for networks with arbitrary unidirectional
networks with unique identifiers that exhibits polynomial space and time
complexity in asynchronous scheduling. We complement the study with
probabilistic protocols for the uniform case: the first probabilistic protocol
requires infinite memory but copes with asynchronous scheduling, while the
second probabilistic protocol has polynomial space complexity but can only
handle synchronous scheduling. Both probabilistic solutions have expected
polynomial time complexity
Self-stabilizing K-out-of-L exclusion on tree network
In this paper, we address the problem of K-out-of-L exclusion, a
generalization of the mutual exclusion problem, in which there are units
of a shared resource, and any process can request up to units
(). We propose the first deterministic self-stabilizing
distributed K-out-of-L exclusion protocol in message-passing systems for
asynchronous oriented tree networks which assumes bounded local memory for each
process.Comment: 15 page
A Survey of Self-Stabilizing Spanning-Tree Construction Algorithms
Self-stabilizing systems can automatically recover from arbitrary state perturbations in finite time. They are therefore well-suited for dynamic, failure prone environments. Spanning-tree construction in distributed systems is a fundamental task which forms the basis for many other network algorithms (like token circulation or routing).This paper surveys self-stabilizing algorithms that construct a spanning tree within a network of processing entities. Lower bounds and related work are also discussed
A Survey of Self-Stabilizing Spanning-Tree Construction Algorithms
Self-stabilizing systems can automatically recover from arbitrary state perturbations in finite time. They are therefore well-suited for dynamic, failure prone environments. Spanning-tree construction in distributed systems is a fundamental task which forms the basis for many other network algorithms (like token circulation or routing).This paper surveys self-stabilizing algorithms that construct a spanning tree within a network of processing entities. Lower bounds and related work are also discussed
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