Abstract
We propose a silent self-stabilizing leader election algorithm for bidirectional arbitrary connected identified networks. This algorithm is written in the locally shared memory model under the distributed unfair daemon. It requires no global knowledge on the network. Its stabilization time is in Θ(n3) steps in the worst case, where n is the number of processes. Its memory requirement is asymptotically optimal, i.e., Θ(logn) bits per processes. Its round complexity is of the same order of magnitude — i.e., Θ(n) rounds — as the best existing algorithms designed with similar settings. To the best of our knowledge, this is the first self-stabilizing leader election algorithm for arbitrary identified networks that is proven to achieve a stabilization time polynomial in steps. By contrast, we show that the previous best existing algorithms designed with similar settings stabilize in a non-polynomial number of steps in the worst case.
Highlights
In distributed computing, the leader election problem consists in distinguishing a single process, so-called the leader, among the others
Starting from an arbitrary configuration, LE converges to a terminal configuration, where the process of minimum ID, l, is elected
To prove the self-stabilization of Algorithm LE under an unfair daemon, we first show that any execution is finite (Theorem 1) and we show that in any terminal configuration, there is a unique leader: for every two processes, p and q, we have Leader(p) = Leader(q) and Leader(p) is the ID of some process (Theorem 2)
Summary
The leader election problem consists in distinguishing a single process, so-called the leader, among the others. The algorithm proposed by Dolev and Herman [14] is not silent, works under a fair daemon, and assume that all processes know a bound N on the number of processes This solution stabilizes in O(D) rounds using Θ(N log N ) bits per process. The algorithm of Arora and Gouda [2] works under a weakly fair daemon and assume the knowledge of some bound N on the number of processes This solution stabilizes in O(N ) rounds using Θ(log N ) bits per process. Datta et al [8] propose the first self-stabilizing leader election algorithm (for arbitrary connected identified networks) proven under the distributed unfair daemon.
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