From adaptive renaming to set agreement

• Published in: Theoretical computer science Vol. 410; no. 14; pp. 1328 - 1335
• Main Authors: Gafni, Eli, Mostéfaoui, Achour, Raynal, Michel, Travers, Corentin
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 28.03.2009; Elsevier
• Subjects: [formula omitted]-resilient algorithm; Adaptive renaming; Asynchronous algorithm; Atomic register; Atomic snapshot; Participating process; Reduction; Set agreement; Shared object; Wait-free algorithm; Reduction; Set agreement; Shared object; Wait-free algorithm; Adaptive renaming; Participating process; t -resilient algorithm; Asynchronous algorithm; Atomic snapshot; Atomic register
• ISSN: 0304-3975; 1879-2294
• DOI: 10.1016/j.tcs.2008.05.016

The adaptive M -renaming problem consists of providing processes with a new name taken from a name space whose size M depends only on the number p of processes that participate in the renaming (and not on the total number n of processes that could ask for a new name). The k -set agreement problem allows each process that proposes a value to decide a proposed value in such a way that at most k different values are decided. In an asynchronous system prone to up to t process crash failures, and where processes can cooperate by accessing atomic read/write registers only, the best that can be done is a renaming space of size M = p + t . In the same setting, the k -set agreement problem cannot be solved when t ≥ k . This paper focuses on the way a solution to the adaptive renaming problem can help in solving the k -set agreement problem when t ≥ k . It has two contributions. Considering the case k = t ( 1 ≤ t < n ), the first contribution is a t -resilient algorithm that solves the k -set agreement problem from any adaptive ( p + k − 1 ) -renaming algorithm. The second contribution considers the case k < t . It shows that there is no such wait-free algorithm when k < n / 2 (wait-free means t = n − 1 ). So, while a solution to the adaptive ( p + k − 1 ) -renaming problem allows t -resiliently solving the k -set agreement problem despite t = k failures, when k < t such an additional power becomes useless for the values of n > 2 k (i.e. adaptive ( p + k − 1 ) -renaming allows progressing from k > t to k = t , but does not allow bypassing the “ k = t ” frontier when n > 2 k ).