Snap-Stabilizing Committee Coordination

Abstract

Abstract-In this paper, we propose two snap-stabilizing distributed algorithms for the committee coordination problem. In this problem, any committee consists of a set of processes and committee meetings are synchronized, so that each process participates in at most one committee meeting at any time. Snap-stabilization is a versatile technique allowing to design algorithms that efficiently tolerate transient faults. Indeed, after a finite number of such faults (e.g. memory corruptions, message losses, etc), a snap-stabilizing algorithm immediately operates correctly, without any external intervention.We design snap-stabilizing committee coordination algorithms enriched with some desirable properties related to concurrency, (weak) fairness, and a stronger synchronization mechanism called 2-Phase Discussion Time. From previous papers, we know that (1) in the general case, (weak) fairness cannot be achieved in the committee coordination, (2) however, it becomes feasible provided that each process waits for meetings infinitely often. Nevertheless, we show that even under this latter assumption, it is impossible to implement a fair solution that allows the best level of concurrency, so called the maximal concurrency. Hence, we propose two orthogonal snapstabilizing algorithms each satisfying, 2-phase discussion time, and either maximal concurrency or fairness. The algorithm implementing fairness requires that every process waits for meetings infinitely often. Moreover, for this algorithm, we introduce and evaluate a new efficiency criterion called the degree of fair concurrency. This criterion shows that even if it does not satisfy maximal concurrency, our snap-stabilizing fair algorithm still allows a high level of concurrency.

Concurrency in snap-stabilizing local resource allocation

“…However, we showed that strong concurrency (an high, but not maximal, level of concurrency) can be achieved by a snap-stabilizing LRA algorithm. We have to underline that the level of concurrency we achieve here is similar to the one obtained in the committee coordination problem [4]. Defining the exact class of resource allocation problems where maximal concurrency (resp.…”

“…This property is called avoiding -deadlock and is informally defined as follows: "if fewer than processes are executing their critical section, 1 then it is possible for another process to enter its critical section, even though no process leaves its critical section in the meantime." Some other properties, inspired from the avoiding -deadlock property, have been proposed to capture the level of concurrency in other resource allocation problems, e.g., k-out-of--exclusion [9] and committee coordination [4]. However, until now, all existing properties of concurrency are specific to a particular problem, e.g., the avoiding -deadlock property cannot be applied to committee coordination.…”

The expressive power of snap-stabilization

“…Snap-stabilization has been also addressed to solve other problems in various contexts, e.g., computing binary search trees [16], cutset detection [17], neighborhood synchronization in trees [18], global synchronization in trees [19], committee coordination [20], computing prefix trees in Peer-to-peer systems [21], and linear message forwarding [22,23,24]. Notice that [24] constitutes the first attempt to deal with snap-stabilization in the context of dynamic networks.…”