670 research outputs found
Polynomial Silent Self-Stabilizing p-Star Decomposition
We present a silent self-stabilizing distributed algorithm computing a maximal p-star decomposition of the underlying communication network. Under the unfair distributed scheduler, the most general scheduler model, the algorithm converges in at most 12∆m + O(m + n) moves, where m is the number of edges, n is the number of nodes, and ∆ is the maximum node degree. Regarding the move complexity, our algorithm outperforms the previously known best algorithm by a factor of ∆. While the round complexity for the previous algorithm was unknown, we show a 5 [n/(p+1)] + 5 bound for our algorithm
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
Optimal Space Lower Bound for Deterministic Self-Stabilizing Leader Election Algorithms
Given a boolean predicate ? on labeled networks (e.g., proper coloring, leader election, etc.), a self-stabilizing algorithm for ? is a distributed algorithm that can start from any initial configuration of the network (i.e., every node has an arbitrary value assigned to each of its variables), and eventually converge to a configuration satisfying ?. It is known that leader election does not have a deterministic self-stabilizing algorithm using a constant-size register at each node, i.e., for some networks, some of their nodes must have registers whose sizes grow with the size n of the networks. On the other hand, it is also known that leader election can be solved by a deterministic self-stabilizing algorithm using registers of O(log log n) bits per node in any n-node bounded-degree network. We show that this latter space complexity is optimal. Specifically, we prove that every deterministic self-stabilizing algorithm solving leader election must use ?(log log n)-bit per node registers in some n-node networks. In addition, we show that our lower bounds go beyond leader election, and apply to all problems that cannot be solved by anonymous algorithms
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
Beeping a Maximal Independent Set
We consider the problem of computing a maximal independent set (MIS) in an
extremely harsh broadcast model that relies only on carrier sensing. The model
consists of an anonymous broadcast network in which nodes have no knowledge
about the topology of the network or even an upper bound on its size.
Furthermore, it is assumed that an adversary chooses at which time slot each
node wakes up. At each time slot a node can either beep, that is, emit a
signal, or be silent. At a particular time slot, beeping nodes receive no
feedback, while silent nodes can only differentiate between none of its
neighbors beeping, or at least one of its neighbors beeping.
We start by proving a lower bound that shows that in this model, it is not
possible to locally converge to an MIS in sub-polynomial time. We then study
four different relaxations of the model which allow us to circumvent the lower
bound and find an MIS in polylogarithmic time. First, we show that if a
polynomial upper bound on the network size is known, it is possible to find an
MIS in O(log^3 n) time. Second, if we assume sleeping nodes are awoken by
neighboring beeps, then we can also find an MIS in O(log^3 n) time. Third, if
in addition to this wakeup assumption we allow sender-side collision detection,
that is, beeping nodes can distinguish whether at least one neighboring node is
beeping concurrently or not, we can find an MIS in O(log^2 n) time. Finally, if
instead we endow nodes with synchronous clocks, it is also possible to find an
MIS in O(log^2 n) time.Comment: arXiv admin note: substantial text overlap with arXiv:1108.192
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
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
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