Mutual exclusion in fully anonymous shared memory systems

An anonymous shared memory REG can be seen as an array of atomic registers such that there is no a priori agreement among the processes on the names of the registers. As an example a very same physical register can be known as REG[x] by a process p and as REG[y] (where y x) by another process q. Moreover, the register known as REG[a] by a process p and the register known as REG[b] by a process q can be the same physical register. It is assumed that each process has a unique identifier that can only be compared for equality. This article is on solving the d-election problem, in which it is required to elect at least one and at most d leaders, in such an anonymous shared memory system. We notice that the 1-election problem is the familiar leader election problem.Let n be the number of processes and m the size of the anonymous memory (number of atomic registers). The article shows that the condition gcd(m, n) ≤ d is necessary and sufficient for solving the d-election problem, where communication is through read/write or read+modify+write registers. The algorithm used to prove the sufficient condition relies on Bezout's Identity -a Diophantine equation relating numbers according to their Greatest Common Divisor. Furthermore, in the process of proving the sufficient condition, it is shown that 1-leader election can be solved using only a single read/write register (which refutes a 1989 conjecture stating that three non-anonymous registers are necessary), and that the exact d-election problem, where exactly d leaders must be elected, can be solved if and only if gcd(m, n) divides d.

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“…Finally, fully anonymous shared memory systems, where both processes and memory are anonymous, were recently investigated in [17,18].…”

Section: Motivation Content and Related Workmentioning

confidence: 99%

From Bezout's Identity to Space-Optimal Election in Anonymous Memory Systems

Godard

Imbs

Raynal

et al. 2020

Proceedings of the 39th Symposium on Principles of Distributed Computing

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“…This constraint is equivalent to ensuring the active nodes form a distance d = 3 independent set from graph theory and is related to the more general (α, β)-ruling sets, originally introduced in [5] and more recently solved under the LOCAL and CONGEST models [33,44]; however, these distributed algorithms rely on static topologies, unique identifiers, and synchronous message delivery. The recent results on mutual exclusion for fully anonymous systems [42] are also related since, like our nodes and their neighborhoods, neither the processes nor the shared resources have unique identifiers. However, like the earlier classical results above and other recent models of weak finite automata [21,22], these do not extend to dynamic network topologies.…”

Section: Related Workmentioning

confidence: 99%

Local Mutual Exclusion for Dynamic, Anonymous, Bounded Memory Message Passing Systems

Daymude¹,

Richa²,

Scheideler³

2021

Preprint

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Mutual exclusion is a classical problem in distributed computing that provides isolation among concurrent action executions that may require access to the same shared resources. Inspired by algorithmic research on distributed systems of weakly capable entities whose connections change over time, we address the local mutual exclusion problem that tasks each node with acquiring exclusive locks for itself and the maximal subset of its "persistent" neighbors that remain connected to it over the time interval of the lock request. Using the established time-varying graphs model to capture adversarial topological changes, we propose and rigorously analyze a local mutual exclusion algorithm for nodes that are anonymous and communicate via asynchronous message passing. The algorithm satisfies mutual exclusion (non-intersecting lock sets) and lockout freedom (eventual success) under both semi-synchronous and asynchronous concurrency. It requires O(∆ log ∆) memory per node and messages of size O(log ∆), where ∆ is the maximum number of connections per node. For systems of weak entities, ∆ is often a small constant, reducing the memory and message size requirements to O(1). We conclude by describing how our algorithm can be used to implement the schedulers assumed by population protocols and the concurrency control operations assumed by the canonical amoebot model, demonstrating its utility in both passively and actively dynamic distributed systems.

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“…-There is a deadlock-free mutual exclusion algorithm in the process anonymous and memory anonymous RMW model made up of m registers if and only if m ∈ M (n). Moreover, there is no such algorithm in the fully anonymous RW communication model [23].…”

Section: Related Work On Anonymous Memoriesmentioning

confidence: 99%

Election in Fully Anonymous Shared Memory Systems: Tight Space Bounds and Algorithms

Imbs¹,

Raynal²,

Taubenfeld³

2022

Preprint

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This article addresses election in fully anonymous systems made up of n asynchronous processes that communicate through atomic read-write registers or atomic read-modify-write registers. Given an integer d ∈ {1, . . . , n − 1}, two elections problems are considered: d-election (at least one and at most d processes are elected) and exact d-election (exactly d processes are elected). Full anonymity means that both the processes and the shared registers are anonymous. Memory anonymity means that the processes may disagree on the names of the shared registers. That is, the same register name A can denote different registers for different processes, and the register name A used by a process and the register name B used by another process can address the same shared register. Let n be the number of processes, m the number of atomic read-modify-write registers, and let M (n, d) = {k : ∀ : 1 < ≤ n : gcd( , k) ≤ d}. The following results are presented for solving election in such an adversarial full anonymity context.-is possible to solve d-election when participation is not required if and only if m ∈ M (n, d). -It is possible to solve exact d-election when participation is required if and only if gcd(m, n) divides d. -It is possible to solve d-election when participation is required if and only if gcd(m, n) ≤ d. -Neither d-election nor exact d-election (be participation required or not) can be solved when the processes communicate through read-write registers only.

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Mutual exclusion in fully anonymous shared memory systems

Cited by 13 publications

References 21 publications

From Bezout's Identity to Space-Optimal Election in Anonymous Memory Systems

From Bezout's Identity to Space-Optimal Election in Anonymous Memory Systems

Local Mutual Exclusion for Dynamic, Anonymous, Bounded Memory Message Passing Systems

Election in Fully Anonymous Shared Memory Systems: Tight Space Bounds and Algorithms

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