Chasing the Weakest System Model for Implementing Ω and Consensus

Abstract

Aguilera et al. and Malkhi et al. presented two system models, which are weaker than all previously proposed models where the eventual leader election oracle can be implemented, and thus, consensus can also be solved. The former model assumes unicast steps and at least one correct process with f outgoing eventually timely links, whereas the latter assumes broadcast steps and at least one correct process with f bidirectional but moving eventually timely links. Consequently, those models are incomparable. In this paper, we show that can also be implemented in a system with at least one process with f outgoing moving eventually timely links, assuming either unicast or broadcast steps. It seems to be the weakest system model that allows to solve consensus via -based algorithms known so far. We also provide matching lower bounds for the communication complexity of in this model, which are based on an interesting "stabilization property" of infinite runs. Those results reveal a fairly high price to be paid for this further relaxation of synchrony properties.

Eventual Leader Election with Weak Assumptions on Initial Knowledge, Communication Reliability, and Synchrony

“…A new assumption that is weaker than both of them, namely eventually moving t-source, is proposed in [23]. An eventually moving t-source is a correct process such that, eventually, each message it sends is timely received by a set Q of t processes (a faulty process is assumed to always receive the messages timely), that can be different at distinct times.…”

“…An eventually moving t-source is a correct process such that, eventually, each message it sends is timely received by a set Q of t processes (a faulty process is assumed to always receive the messages timely), that can be different at distinct times. In [23] three Ω protocols based on an eventually moving t-source are presented. A lower bound of Ω (nt) on the communication complexity (links that carry messages forever) of any protocol based on an eventually moving t-source is also given.…”

Specifying and implementing an eventual leader service for dynamic systems

“…According to the maximal number of processes that can crash, the number of eventually synchronous links, their structure, the fact they can change with time, etc., different assumptions have been proposed and algorithms based on these assumptions have been designed. Examples of such assumptions and algorithms can be found in [3,4,5,6,9,15,16,17].…”

Failure Detectors Encapsulate Fairness

“…Despite such uncertainty, partial synchrony is useful for solving problems in crash-prone distributed systems, and several such models have been proposed in the literature (e.g., [18,17,26,27,[39][40][41]). These models vary in the information they provide about these bounds, and consequently they have different crash detection capabilities.…”