Search

The failure detector abstraction has been used to solve agreement problems in asynchronous systems prone to crash failures, but so far it has mostly been used in static and complete networks. This paper aims to adapt existing failure detectors in order to solve agreement problems in unknown, dynamic systems. We are specifically interested in the k-set agreement problem. The problem of k-set agreement is a generalization of consensus where processes can decide up to k different values. Although some solutions to this problem have been proposed in dynamic networks, they rely on communication synchrony or make strong assumptions on the number of process failures. In this paper we consider unknown dynamic systems modeled using the formalism of Time-Varying Graphs, and extend the definition of the existing \Pi \Sigma x,y failure detector to obtain the \Pi \Sigma \bot, x,y failure detector, which is sufficient to solve k-set agreement in our model. We then provide an implementation of this new failure detector using connectivity and message pattern assumptions. Finally, we present an algorithm using \Pi \Sigma \bot, x,y to solve k-set agreement. [ABSTRACT FROM AUTHOR]

A notion of a universal construction suited to distributed computing has been introduced by Herlihy in his celebrated paper ' Wait-free synchronization' (ACM Trans Program Lang Syst 13(1):124-149, 1991). A universal construction is an algorithm that can be used to wait-free implement any object defined by a sequential specification. Herlihy's paper shows that the basic system model, which supports only atomic read/write registers, has to be enriched with consensus objects to allow the design of universal constructions. The generalized notion of a k -universal construction has been recently introduced by Gafni and Guerraoui (Proceedings of 22nd international conference on concurrency theory (CONCUR'11), Springer LNCS 6901, pp 17-27, 2011). A k-universal construction is an algorithm that can be used to simultaneously implement k objects (instead of just one object), with the guarantee that at least one of the k constructed objects progresses forever. While Herlihy's universal construction relies on atomic registers and consensus objects, a k-universal construction relies on atomic registers and k-simultaneous consensus objects (which are wait-free equivalent to k-set agreement objects in the read/write system model). This paper significantly extends the universality results introduced by Herlihy and Gafni-Guerraoui. In particular, we present a k-universal construction which satisfies the following five desired properties, which are not satisfied by the previous k-universal construction: (1) among the k objects that are constructed, at least $$\ell $$ objects (and not just one) are guaranteed to progress forever; (2) the progress condition for processes is wait-freedom, which means that each correct process executes an infinite number of operations on each object that progresses forever; (3) if any of the k constructed objects stops progressing, all its copies (one at each process) stop in the same state; (4) the proposed construction is contention-aware, in the sense that it uses only read/write registers in the absence of contention; and (5) it is generous with respect to the obstruction-freedom progress condition, which means that each process is able to complete any one of its pending operations on the k objects if all the other processes hold still long enough. The proposed construction, which is based on new design principles, is called a $$(k,\ell )$$ -universal construction. It uses a natural extension of k-simultaneous consensus objects, called $$(k,\ell )$$ -simultaneous consensus objects ( $$(k,\ell )$$ -SC). Together with atomic registers, $$(k,\ell )$$ -SC objects are shown to be necessary and sufficient for building a $$(k,\ell )$$ -universal construction, and, in that sense, $$(k,\ell )$$ -SC objects are $$(k,\ell )$$ - $$ {universal}$$ . [ABSTRACT FROM AUTHOR]