Brief Announcement: Memory Lower Bounds for Self-Stabilization

Blin, Lélia; Feuilloley, Laurent; Bouder, Gabriel Le

doi:10.4230/lipics.disc.2019.37

Cited by 2 publications

(1 citation statement)

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“…The model considered in this paper bears similarities with some models used in the context of self-stabilization. Many papers (see, e.g., [9,10,11,12]) have addressed the design of self-stabilizing algorithms for 3-coloring the cycles, or for (𝛥 + 1)-coloring graphs with maximum degree 𝛥. Self-stabilization assumes that the processing elements can behave arbitrarily bad (all variables can be corrupted). The objective is to design algorithms which, starting from an arbitrary initial configuration, eventually compute a legal configuration (e.g., a configuration in which the colors assigned to the nodes form a proper coloring) whenever no failures occur during a sufficiently long period.…”

Section: Related Workmentioning

confidence: 99%

Fault Tolerant Coloring of the Asynchronous Cycle

Fraigniaud¹,

Lambein-Monette²,

Rabie³

2022

Preprint

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We present a wait-free algorithm for proper coloring the 𝑛 nodes of the asynchronous cycle 𝐶 𝑛 , where each crash-prone node starts with its (unique) identifier as input. The algorithm is independent of 𝑛 ⩾ 3, and runs in O(log * 𝑛) rounds in 𝐶 𝑛 . This round-complexity is optimal thanks to a known matching lower bound, which applies even to synchronous (failure-free) executions. The range of colors used by our algorithm, namely { 0, . . . , 4 }, is optimal too, thanks to a known lower bound on the minimum number of names for which renaming is solvable wait-free in shared-memory systems, whenever 𝑛 is a power of a prime. Indeed, our model coincides with the shared-memory model whenever 𝑛 = 3, and the minimum number of names for which renaming is possible in 3-process shared-memory systems is 5. ACM Subject ClassificationTheory of computation → Distributed algorithms; Mathematics of computing → Graph coloring; Computer systems organization → Dependable and fault-tolerant systems and networks; Theory of computation → Models of computation Keywords and phrases graph coloring, LOCAL model, shared-memory model, immediate snapshot, renaming, wait-free algorithms.

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Section: Related Workmentioning

confidence: 99%