A Thin Self-Stabilizing Asynchronous Unison Algorithm with Applications to Fault Tolerant Biological Networks

Emek, Yuval; Keren, Eyal

doi:10.1145/3465084.3467922

Cited by 8 publications

(9 citation statements)

References 22 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Known self-stabilizing MIS algorithms for the beeping model require (approximate) knowledge of n, use space that is a super-constant function of n, and require a super-constant number of random bits [1,23,16]. In the stone age model, an MIS algorithm proposed in [13] has similar properties as our algorithms (and is provably fast for all graphs) but is not self-stabilizing; while a self-stabilizing algorithm for the model proposed recently in [12] is fast only on graphs whose diameter is bounded by a known constant D. Other randomized self-stabilizing MIS algorithms required super constant state and communication [30]. Finally, known deterministic self-stabilizing MIS algorithms require distinct node IDS, super constant state and communication, and are in general much slower than the randomized algorithms, stabilizing in time linear in n or in the maximum degree ∆ [22,18,29,5].…”

Section: Introductionmentioning

confidence: 81%

“…on G n,p for all 0 ≤ p ≤ 1. The extended process uses a phase clock sub-process proposed in [12]. Interestingly, unlike [12], we do not use the phase clock for synchronization, but rather as a local non-synchronized counter (see Section 1.2 for a more detailed discussion).…”

Section: Our Contributionmentioning

confidence: 99%

“…We also propose a simple variant of the 2-state MIS process, called the 3-state MIS process, which has an additional state and does not require collision detection (see Definition 5). This variant is suitable for the synchronous stone age model [13,12]. The synchronous stone age model can be viewed as an extension of the beeping model over a constant number of channels (without collision detection): each node beeps in at most one channel and listens to the other channels.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Distributed Self-Stabilizing MIS with Few States and Weak Communication

Giakkoupis¹,

Ziccardi²

2023

Preprint

View full text Add to dashboard Cite

We study a simple random process that computes a maximal independent set (MIS) on a general n-vertex graph. Each vertex has a binary state, black or white, where black indicates inclusion into the MIS. The vertex states are arbitrary initially, and are updated in parallel: In each round, every vertex whose state is "inconsistent" with its neighbors', i.e., it is black and has a black neighbor, or it is white and all neighbors are white, changes its state with probability 1/2. The process stabilizes with probability 1 on any graph, and the resulting set of black vertices is an MIS. It is also easy to see that the expected stabilization time is O(log n) on certain graph families, such as cliques and trees. However, analyzing the process on graphs beyond these simple cases seems challenging.Our main result is that the process stabilizes in poly(log n) rounds w.h.p. on G n,p random graphs, for 0 ≤ p ≤ poly(log n) • n −1/2 and p ≥ 1/ poly(log n). Further, an extension of this process, with larger but still constant vertex state space, stabilizes in poly(log n) rounds on G n,p w.h.p., for all 1 ≤ p ≤ 1. We conjecture that this improved bound holds for the original process as well. In fact, we believe that the original process stabilizes in poly(log n) rounds on any given n-vertex graph w.h.p. Both processes readily translate into distributed/parallel MIS algorithms, which are self-stabilizing, use constant space (and constant random bits per round), and assume restricted communication as in the beeping or the synchronous stone age models. To the best of our knowledge, no previously known MIS algorithm is self-stabilizing, uses constant space and constant randomness, and stabilizes in poly(log n) rounds in general or random graphs.

show abstract

Section: Introductionmentioning

confidence: 81%

Section: Our Contributionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Distributed Self-Stabilizing MIS with Few States and Weak Communication

Giakkoupis¹,

Ziccardi²

2023

Preprint

View full text Add to dashboard Cite

show abstract

“…As one of the synchronization problems, for global mutual exclusion problem, much research has been devoted to self-stabilizing algorithms, e.g., [14] and [15]. Self-stabilizing distributed algorithms for the local (group) mutual exclusion problem are proposed in [5][6][7]9]. Various generalized versions of mutual exclusion have been studied extensively, e.g., l-mutual exclusion [16,17], mutual inclusion [18] 1 , l-mutual inclusion [18], critical section problem [19,20].…”

Section: Related Workmentioning

confidence: 99%

“…To solve the NMR consistently, the processes should schedule the operations carefully. One may think we can apply mutual exclusion [3], local mutual exclusion [4][5][6][7], or local group mutual exclusion [8][9][10] to solve the local synchronization problem. Mutual exclusion (resp., local mutual exclusion) guarantees that no two processes (resp., no two neighboring processes) enter a critical section (CS) at the same time.…”

Section: Introductionmentioning

confidence: 99%

Neighborhood Mutual Remainder:Self-Stabilizing Distributed Implementationand Applications

Kamei

Katayama

Ooshita

et al. 2022

Preprint

View full text Add to dashboard Cite

This paper considers a situation where each process has a set of operations Op and executes each operation in Op infinitely often in distributed systems. Then, let Oe ⊂ Op be a subset of operations, which cannot be executed by a process while its closed neighborhood execute operations in Op∖ Oe. For such a situation, this new concept of Neighborhood Mutual Remainder (NMR) is defined. A distributed algorithm that satisfies the NMR requirement should satisfy the following two properties:(1) Liveness is satisfied if a process executes each operation in Op infinitely often, and (2) safety is satisfied if, when each process executes operations in Oe, no process in its closed neighborhood executes operations in Op∖ Oe. We formalize the concept of NMR and give a simple self-stabilizing algorithm to demonstrate the design paradigm to achieve NMR. We present an application of NMR to a LOOK-COMPUTE-MOVE (LCM) robot system for implementing a move-atomic property, where robots possess an independent clock that is advanced at the same speed. It is the first self-stabilizing implementations of the LCM synchronization for environments where each robot can have limited visibility and lights.

show abstract