Self-stabilizing Leader Election Research Articles

ANALYSIS OF THE AVERAGE EXECUTION TIME FOR A SELF-STABILIZING LEADER ELECTION ALGORITHM

This paper focuses on the self-stabilizing leader election algorithm of Xu and Srimani [10] that finds a leader in a tree graph. The worst case execution time for this algorithm is O(N4), where N is the number of nodes in the tree. We show that the average execution time for this algorithm, assuming two different scenarios, is much lower than O(N4). In the first scenario, the algorithm assumes an equiprobable daemon and it only privileges a single node at a time. The average execution time for this case is O(N2). For the second case, the algorithm can privilege multiple nodes at a time. We eliminate the daemon from this algorithm by making random choices to avoid interference between neighboring nodes. The execution time for this case is O(N). We also show that for specific tree graphs, these results reduce even more.

A Self-Stabilizing Leader Election Algorithm in Highly Dynamic Ad Hoc Mobile Networks

The classical definition of a self-stabilizing algorithm assumes generally that there are no faults in the system long enough for the algorithm to stabilize. Such an assumption cannot be applied to ad hoc mobile networks characterized by their highly dynamic topology. In this paper, we propose a self-stabilizing leader election algorithm that can tolerate multiple concurrent topological changes. By introducing the time-interval-based computation concept, the algorithm ensures that a network partition can within a finite time converge to a legitimate state even if topological changes occur during the convergence time. Our simulation results show that our algorithm can ensure that each node has a leader over 99 percent of the time. We also give an upper bound on the frequency at which network components merge to guarantee the convergence.

Randomized self-stabilizing and space optimal leader election under arbitrary scheduler on rings

We present a randomized self-stabilizing leader election protocol and a randomized self-stabilizing token circulation protocol under an arbitrary scheduler on anonymous and unidirectional rings of any size. These protocols are space optimal. We also give a formal and complete proof of these protocols. To this end, we develop a complete model for probabilistic self-stabilizing distributed systems which clearly separates the non deterministic behavior of the scheduler from the randomized behavior of the protocol. This framework includes all the necessary tools for proving the self- stabilization of a randomized distributed system: definition of a probabilistic space and definition of the self-stabilization of a randomized protocol. We also propose a new technique of scheduler management through a self-stabilizing protocol composition (cross-over composition). Roughly speaking, we force all computations to have a fairness property under any scheduler, even under an unfair one.

SELF-STABILIZING ANONYMOUS LEADER ELECTION IN A TREE

We propose a new self-stabilizing anonymous leader election algorithm in a tree graph. We show the correctness of the protocol and show that the protocol terminates in O(n4) time starting from any arbitrary initial state. The protocol can elect either a leaf node or a non leaf node (starting from the same initial state) depending on the behavior of the daemon. The protocol generalizes the result in [1] and at the same time is much simpler and terminates in polynomial number of moves.

Uniform dynamic self-stabilizing leader election

A distributed system is self-stabilizing if it can be started in any possible global state. Once started the system regains its consistency by itself, without any kind of outside intervention. The self-stabilization property makes the system tolerant to faults in which processors exhibit a faulty behavior for a while and then recover spontaneously in an arbitrary state. When the intermediate period in between one recovery and the next faulty period is long enough, the system stabilizes. A distributed system is uniform if all processors with the same number of neighbors are identical. A distributed system is dynamic if it can tolerate addition or deletion of processors and links without reinitialization. In this work, we study uniform dynamic self-stabilizing protocols for leader election under readwrite atomicity. Our protocols use randomization to break symmetry. The leader election protocol stabilizes in O(/spl Delta/D log n) time when the number of the processors is unknown and O(/spl Delta/D), otherwise. Here /spl Delta/ denotes the maximal degree of a node, D denotes the diameter of the graph and n denotes the number of processors in the graph. We introduce self-stabilizing protocols for synchronization that are used as building blocks by the leader-election algorithm. We conclude this work by presenting a simple, uniform, self-stabilizing ranking protocol.

An exercise in fault-containment: Self-stabilizing leader election

Self-stabilizing algorithms are designed to guarantee convergence to some desired stable state from arbitrary initial states arising out of an arbitrarily large number of faults. However, in a well-designed system, the simultaneous occurrence of a large number of faults is rare. It is therefore desirable to design algorithms that are not only self-stabilizing, but also have the ability to recover very fast from a bounded number of faults. As an illustration, we present a simple self-stabilizing leader election protocol that recovers in O(1) time from a state with a single transient fault on oriented rings. Only the faulty node and its two neighbors change their state during convergence to a stable state. Thus, the effect of a single fault is tightly contained around the fault. The technique for transforming a self-stabilizing algorithm into its fault-contained version is simple and general, and can be applied to other problems as well that satisfy certain properties.

A Self-Stabilizing Leader Election Algorithm for Tree Graphs

We propose a self-stabilizing algorithm (protocol) for leader election in a tree graph. We show the correctness of the proposed algorithm by using a new technique involving induction.

Leader election in uniform rings

A self-stabilizing leader election protocol is proposed here for uniform rings of primal size. A ring of processors is said to be uniform if no distinguished leader processor exists. Having the proposed protocol as the first phase, all self-stabilizing protocols for nonuniform rings can be implemented as the second phase. Dijkstra's self-stabilizing mutual exclusion protocol for nonuniform rings is superimposed as an example on the leader election protocol. The result is a two-phase self-stabilizing mutual exclusion protocol for uniform rings. Let the size of the ring be n. Our self-stabilizing mutual exclusion protocol uses 3n states for each processor, which improves a previous result that uses approximately (n 2 /ln n) states