Local Terminations and Distributed Computability in Anonymous Networks

Abstract

Abstract. We investigate the computability of distributed tasks in reliable anonymous networks with arbitrary knowledge. More precisely, we consider tasks computable with local termination, i.e., a node knows when to stop to participate in a distributed algorithm, even though the algorithm is not necessarily terminated elsewhere. We also study weak local termination, that is when a node knows its final value but continues to execute the distributed algorithm, usually in order to provide information to other nodes. We give the first characterization of distributed tasks that can be computed with weak local termination and we present a new characterization of tasks computed with local termination. For both terminations, we also characterize tasks computable by polynomial algorithms.

Efficient distributed snapshots in an anonymous asynchronous message-passing system

“…This is really the concurrent snapshot initiation problem, and the snapshot termination detection problem bundled together as a single problem. Termination detection of distributed computations has been studied independently in many works [5,12,17], but not in conjunction with the snapshot recording problem, except in the algorithm by Chalopin et al [6]. The Chalopin et al algorithm records a global snapshot under concurrent initiators and also determines the global termination of the snapshot recording activity in an anonymous system, by superimposing the termination detection algorithm of Szymanski et al [20] on the Chandy-Lamport snapshot recording algorithm.…”

Snap-Stabilizing Tasks in Anonymous Networks

“…This condition is given in Theorem 3. It is the same as the one given in [CGM08] for solvability with explicit termination. We first prove our results for terminating tasks in the asynchronous model, then we show how to extend the technique for long lived tasks in the synchronous model (for simplicity of exposition).…”

“…Given a distributed task, the condition for it being solvable by an algorithm with explicit termination was first given in [BV01]. The presentation we will use in this paper is the one given in [CGM08]. Instead of the View algorithm of [YK96,BV01], we use Mazurkiewicz' algorithm [Maz97].…”

“…On the distributed computability side, the first complete characterization of tasks that admits self-stabilizing algorithms has been given in [BV02b]. Here, we use a mix of different techniques from the second approach, some of which were first introduced in [CGM08].…”

On mobile agent verifiable problems

“…A different approach considers the characterization of problems that can be solved under various notions of termination detection or various types of knowledge about the network in message-passing systems [3,4,6,7,28]. Finally, recent works focus on the computational power of teams of mobile agents [10,19].…”