Failure detectors - oracles that provide information about process crashes - are an important abstraction for crash tolerance in distributed systems. Although current failure-detector theory provides great generality and expressiveness, it also poses significant challenges in developing a robust hierarchy of failure detectors. We address some of these challenges by proposing a variant of failure detectors called asynchronous failure detectors and an associated modeling framework. Unlike the traditional failure-detector framework, our framework eschews real time completely. We show that asynchronous failure detectors are sufficiently expressive to include several popular failure detectors. Additionally, we show that asynchronous failure detectors satisfy many desirable properties: they are self-implementable, guarantee that stronger asynchronous failure detectors solve more problems, and ensure that their outputs encode no information other than process crashes. We introduce the notion of a failure detector being representative of a problem to capture the idea that some problems encode the same information about process crashes as their weakest failure detectors do. We show that a large class of problems, called finite problems, do not have representative failure detectors.

The aggregation problem assumes that every process starts an execution with a unique token (an abstraction for data). The goal is to collect these tokens at a minimum number of processes by the end of the execution. This problem is particularly relevant to mobile networks where peer-to-peer communication is cheap (e.g., using 802.11 or Bluetooth), but uploading data to a central server can be costly (e.g., using 3G/4G). With this in mind, we study this problem in a dynamic network model, in which the communication graph can change arbitrarily from round to round.

Consider a setting where nodes can vary their transmission power thereby changing the network topology, the goal of topology control is to reduce the transmission power while ensuring the communication graph remains connected. Wattenhofer et al. [6] introduced the distributed cone-based topology control algorithm with parameter α (CBTC(α)) and proved it correct if α ≤ 2π/3. Li et al. [4] proposed performing asymmetric edge removal or increasing α to 5π/6, and proved that when applied separately these minimizations preserve connectivity. Bahramgiri et al. [1] proved that when α ≤ 2π/3 it was possible to extend the algorithm to work in three dimensions and described a variation to preserve k-connectivity.

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