Snap-stabilization and PIF in tree networks

Abstract

The contribution of this paper is threefold. First, we present the paradigm of snap-stabilization. A snapstabilizing protocol guarantees that, starting from an arbitrary system configuration, the protocol always behaves according to its specification. So, a snap-stabilizing protocol is a time optimal self-stabilizing protocol (because it stabilizes in 0 rounds). Second, we propose a new Propagation of Information with Feedback (PIF) cycle, called Propagation of Information with Feedback and Cleaning (PFC). We show three different implementations of this new PIF. The first one is a basic PFC cycle which is inherently snap-stabilizing. However, the first PIF cycle can be delayed O(h 2 ) rounds (where h is the height of the tree) due to some undesirable local states. WARNING:The concept of snap-stabilization was first introduced in [12]. The concept evolved over the last eight years. We take this evolution in consideration in this paper, which includes the early results published in [10] and [12]. In particular, infinite repetition of computation cycles is a requirement of self -stabilizing systems. This is not required in snap-stabilization because snap-stabilization ensures that the first completed computation cycle is executed according to the specification of the problem. The correctness proofs conform to this basic property.The second algorithm improves the worst delay of the basic PFC algorithm from O(h 2 ) to 1 round. The state requirement for the above two algorithms is 3 states per processor, except for the root and leaf processors that use only 2 states. Also, they work on oriented trees. We then propose a third snap-stabilizing PIF algorithm on un-oriented tree networks. The state requirement of the third algorithm depends on the degree of the processors, and the delay is at most h rounds. Next, we analyze the maximum waiting time before a PIF cycle can be initiated whether the PIF cycle is infinitely and sequentially repeated or launch as an isolated PIF cycle. The analysis is made for both oriented and un-oriented trees. We show or conjecture that the two best of the above algorithms produce optimal waiting time. Finally, we compute the minimal number of states the processors require to implement a single PIF cycle, and show that both algorithms for oriented trees are also (in addition to being time optimal) optimal in terms of the number of states.

Snap-Stabilizing Committee Coordination

“…Snap-stabilization [6] is a versatile technique that allows designing 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.…”

Best-effort group service in dynamic networks

“…Except if the convergence time is, by construction, null (snap-stabilization [7]), the system cannot determine whether it is in a convergence phase or if the specifications are currently satisfied. As a consequence, self-stabilizing algorithms are mainly useful when the convergence time is much smaller than the delay between two transient faults.…”

Snap-Stabilization in Message-Passing Systems

“…In particular propagation of information with feedback (PIF) is a popular problem to address [11,10,12,20,14,9,19]. Several studies present snap-stabilizing token circulation protocols [30,16,18].…”