Snap-stabilizing Protocol Research Articles

How to improve snap-stabilizing point-to-point communication space complexity?

A snap-stabilizing protocol, starting from any configuration, always behaves according to its specification. In this paper, we are interested in the message forwarding problem in a message-switched network in which the system resources must be managed in order to deliver messages to any processor of the network. To this end, we use the information provided by a routing algorithm. In the context of an arbitrary initialization (due to stabilization), this information may be corrupted. In Cournier et al. (2009) [1], we show that there exist snap-stabilizing algorithms for this problem (in the state model). This implies that we can request the system to begin forwarding messages without losses even if routing information is initially corrupted. In this paper, we propose another snap-stabilizing algorithm for this problem which improves the space complexity of the one in Cournier et al. (2009) [1].

SNAP-STABILIZING PREFIX TREE FOR PEER-TO-PEER SYSTEMS

Several factors still hinder the deployment of computational grids over large scale platforms. Among them, the resource discovery is one crucial issue. New approaches, based on peer-to-peer technologies, tackle this issue. Because they efficiently allow range queries, Tries (a.k.a., Prefix Trees) appear to be among promising ways in the design of distributed data structures indexing resources. Despite their lack of robustness in dynamic settings, trie-structured approaches outperform other peer-to-peer fashioned technologies by efficiently supporting range queries. Within recent trie-based approaches, the fault-tolerance is handled by preventive mechanisms, intensively using replication. However, replication can be very costly in terms of computing and storage resources and does not ensure the recovery of the system after arbitrary failures. Self-stabilization is an efficient approach in the design of reliable solutions for dynamic systems. It ensures a system to converge to its intended behavior, regardless of its initial state, in a finite time. A snap-stabilizing algorithm guarantees that it always behaves according to its specification, once the protocol is launched. In this paper, we provide the first snap-stabilizing protocol for trie construction. We design particular tries called Proper Greatest Common Prefix (PGCP) Tree. The proposed algorithm arranges the n label values stored in the tree, in average, in O(h + h′) rounds, where h and h′ are the initial and final heights of the tree, respectively. In the worst case, the algorithm requires an O(n) extra space on each node, O(n) rounds and O(n2) actions. However, simulations allow to state that this worst case is far from being reached and to confirm the average complexities, showing the practical efficiency of this protocol.

Snap-stabilization and PIF in tree networks

The contribution of this paper is threefold. First, we present the paradigm of snap-stabilization. A snap- stabilizing 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 ( $$\mathcal{PFC}$$ ). We show three different implementations of this new PIF. The first one is a basic $$\mathcal{PFC}$$ 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. The second algorithm improves the worst delay of the basic $$\mathcal{PFC}$$ 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.

Optimal snap-stabilizing depth-first token circulation in tree networks

We address the depth-first token circulation (DFTC) in tree networks. We first consider oriented trees—every processor knows which of its neighbors leads to a particular processor called the root. On such trees, we propose a state optimal DFTC algorithm. Next, we propose a second algorithm, also for trees, but where no processor knows which of its neighbor leads to the root. This algorithm is also optimal in terms of the number of states per processor. Both algorithms works under any daemon, even unfair. Furthermore, both are snap-stabilizing. A snap-stabilizing protocol guarantees that the system always maintains the desirable behavior. In other words, a snap-stabilizing algorithm is also a self-stabilizing algorithm which stabilizes in 0 steps. Thus, both algorithms are also optimal in terms of the stabilization time. Finally, two approaches of the maximum waiting time to initiate a DFTC are also discussed, whether the tree is oriented or not. In every case but one, we show that the waiting time is asymptotically optimal. In the last case, we conjecture the same result.

Snap-Stabilizing Depth-First Search on Arbitrary Networks

A snap-stabilizing protocol, starting from any arbitrary initial configuration, always behaves according to its specification. In this paper, we present the first snap-stabilizing depth-first search wave protocol for arbitrary rooted networks assuming an unfair daemon, i.e. assuming the weakest scheduling assumption (a preliminary version of this work was presented in OPODIS 2004, 8th International Conference on Principles of Distributed Systems, Grenoble (France)).