The South Zone: Distributed Algorithms for Alliances

Dourado, Mitre C.; Penso, Lúcia Draque; Rautenbach, Dieter; Szwarcfiter, Jayme Luiz

doi:10.1007/978-3-642-24550-3_15

Cited by 5 publications

(11 citation statements)

References 21 publications

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“…Then, A is 1-minimal if and only if ∀p ∈ A, A \ {p} is not an (f, g)-alliance. Surprisingly, a 1-minimal (f, g)-alliance is not necessarily a minimal (f, g)-alliance, [5]. However, we have the following property:…”

Section: Preliminariesmentioning

confidence: 79%

“…The possible steps induce a binary relation over configurations of A, denoted by →. An execution of A is a maximal 5 The daemon realizes the asynchrony of the system. sequence of its configurations e = γ 0 γ 1 .…”

Section: Preliminariesmentioning

confidence: 99%

“…The (f, g)-alliance problem is introduced in [5]. In the same paper, the authors give several distributed algorithms for that problem and its variants, but none of them is self-stabilizing.…”

Section: Introductionmentioning

confidence: 99%

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Self-stabilizing (f,g)-Alliances with Safe Convergence

Carrier

Datta

Devismes

et al. 2013

Lecture Notes in Computer Science

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Abstract. Given two functions f and g mapping nodes to non-negative integers, we give a silent self-stabilizing algorithm that computes a minimal (f, g)-alliance in an asynchronous network with unique node IDs, assuming that every node p has a degree at least g(p) and satisfies f (p) ≥ g(p). Our algorithm is safely converging in the sense that starting from any configuration, it first converges to a (not necessarily minimal) (f, g)-alliance in at most four rounds, and then continues to converge to a minimal one in at most 5n+4 additional rounds, where n is the size of the network. Our algorithm is written in the shared memory model. It is proven assuming an unfair (distributed) daemon. Its memory requirement is O(log n) bits per process, and it takes O(∆ 3 n) steps to stabilize, where ∆ is the degree of the network.

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Section: Preliminariesmentioning

confidence: 79%

Section: Preliminariesmentioning

confidence: 99%

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Self-stabilizing (f,g)-Alliances with Safe Convergence

Carrier

Datta

Devismes

et al. 2013

Lecture Notes in Computer Science

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“…Property 1 (Dourado et al [29]) Given two non-negative integer-valued functions f and g on nodes 1. Every minimal (f, g)-alliance is a 1-minimal (f, g)-alliance, and 2. if f (u) ≥ g(u) for every process u, then every 1-minimal (f, g)-alliance is a minimal (f, g)-alliance.…”

Section: The Problemmentioning

confidence: 99%

Self-Stabilizing Distributed Cooperative Reset

Devismes¹,

Johnen²

2019

2019 IEEE 39th International Conference on Distributed Computing Systems (ICDCS)

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Self-stabilization is a versatile fault-tolerance approach that characterizes the ability of a system to eventually resume a correct behavior after any finite number of transient faults. In this paper, we propose a self-stabilizing reset algorithm working in anonymous networks. This algorithm resets the network in a distributed non-centralized manner, i.e., it is multi-initiator, as each process detecting an inconsistency may initiate a reset. It is also cooperative in the sense that it coordinates concurrent reset executions in order to gain efficiency. Our approach is general since our reset algorithm allows to build self-stabilizing solutions for various problems and settings. As a matter of fact, we show that it applies to both static and dynamic specifications since we propose efficient self-stabilizing reset-based algorithms for the (1minimal) (f, g)-alliance (a generalization of the dominating set problem) in identified networks and the unison problem in anonymous networks. Notice that these two latter instantiations enhance the state of the art. Indeed, in the former case, our solution is more general than the previous ones; while in the latter case, the time complexity of the proposed unison algorithm is better than that of previous solutions of the literature. This study was partially supported by the French ANR projects ANR-16-CE40-0023 (DESCARTES) and ANR-16 CE25-0009-03 (ESTATE). version. However, this so-called transformer is, by essence, inefficient both in terms of space and time complexities: actually, its purpose is only to demonstrate the feasibility of the transformation.Interestingly, many proposed general methods [36,7,4,5] are based on reset algorithms. Such algorithms are initiated when an inconsistency is discovered in the network, and aim at reinitializing the system to a correct (pre-defined) configuration.A reset algorithm may be centralized at a leader process (e.g., see [4]), or fully distributed, meaning multi-initiator (as our proposal here). In the former case, either the reset is coupled with a snapshot algorithm (which makes a global checking of the network), or processes detecting an incoherence (using local checking [6]) should request a reset to the leader. In the fully distributed case, resets are locally initiated by processes detecting inconsistencies. This latter approach is considered as more efficient when the concurrent resets are coordinated. In other words, concurrent resets have to be cooperative (in the sense of [37]) to ensure the fast convergence of the system to a consistent global state.Self-stabilization makes no hypotheses on the nature (e.g., memory corruption or topological changes) or extent of transient faults that could hit the system, and a self-stabilizing system recovers from the effects of those faults in a unified manner. Now, such versatility comes at a price, e.g., after transient faults cease, there is a finite period of time, called the stabilization phase, during which the safety properties of the system are violated. Hence, self-stabilizing al...

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“…The most extensively studied are defensive alliances [9,8,13,19,21], offensive alliances [7,12,18] and powerful or dual alliances [2,3,22]. A more generalized concept of alliance is represented by k-alliances [1,15,16,17,19], and Dourado et al presented a new definition of alliances, namely, (f, g)-alliances [6], that generalizes previous concepts. In [23], Yero and Rodríguez-Velázquez published a summary of the major results obtained concerning defensive alliances up through 2013.…”

Section: Introductionmentioning

confidence: 99%