Self-stabilising Priority-Based Multi-Leader Election and Network Partitioning

A common task in situated distributed systems is the self-organising election of leaders. These leaders can be devices or software agents appointed, for instance, to coordinate the activities of other agents or processes. In this work, we focus on the multi-leader election problem in networks of asynchronous message-passing devices, which are a common model in self-organisation approaches like aggregate computing. Specifically, we introduce a novel algorithm for space- and priority-based leader election and compare it with the state of the art. We call the algorithm Bounded Election since it leverages bounding (i.e. minimisation or maximisation) of candidacy messages to drop or promote candidate leaders and ensure stabilisation. The proposed algorithm is formally proven to be self-stabilising, allows for leader prioritisation, and performs on-the-fly network partitioning (namely, as a side effect of the leader election process, the areas regulated by the leaders are also established). Also, we experimentally compare its performance together with the state of the art of leader election in aggregate computing in a variety of synthetic scenarios, showing benefits in terms of convergence time and resilience

Self-stabilized fast gossiping algorithms

In this article, we explore the topic of extending aggregate computation in distributed networks with selfstabilizing properties to withstand network dynamics. Existing research suggests that fast gossiping algorithms, based on the properties of order statistics applied to families of exponential random variables, are a viable solution for computing functions of the values stored in the network. We focus on the specific case in which network changes and failures occur in batches with a minimum frequency in the order of the diameter of the network. Our contribution consists in two self-stabilizing mechanisms, allowing fast gossiping algorithms to be applicable to dynamic networks with minor increase in resources usage. The resulting algorithms can be deployed in networks exhibiting churn, node stop-failures and resets, and random topological changes. The theoretical results are verified with simulations on synthetic data, showcasing desirable properties for large-scale network designers such as scalability, lack of single points of failure, and anonymity

A framework for proving the self-organization of dynamic systems

This paper aims at providing a rigorous definition of self- organization, one of the most desired properties for dynamic systems (e.g., peer-to-peer systems, sensor networks, cooperative robotics, or ad-hoc networks). We characterize different classes of self-organization through liveness and safety properties that both capture information re- garding the system entropy. We illustrate these classes through study cases. The first ones are two representative P2P overlays (CAN and Pas- try) and the others are specific implementations of \Omega (the leader oracle) and one-shot query abstractions for dynamic settings. Our study aims at understanding the limits and respective power of existing self-organized protocols and lays the basis of designing robust algorithm for dynamic systems

Population stability: regulating size in the presence of an adversary

We introduce a new coordination problem in distributed computing that we call the population stability problem. A system of agents each with limited memory and communication, as well as the ability to replicate and self-destruct, is subjected to attacks by a worst-case adversary that can at a bounded rate (1) delete agents chosen arbitrarily and (2) insert additional agents with arbitrary initial state into the system. The goal is perpetually to maintain a population whose size is within a constant factor of the target size $N$. The problem is inspired by the ability of complex biological systems composed of a multitude of memory-limited individual cells to maintain a stable population size in an adverse environment. Such biological mechanisms allow organisms to heal after trauma or to recover from excessive cell proliferation caused by inflammation, disease, or normal development. We present a population stability protocol in a communication model that is a synchronous variant of the population model of Angluin et al. In each round, pairs of agents selected at random meet and exchange messages, where at least a constant fraction of agents is matched in each round. Our protocol uses three-bit messages and $\omega(\log^2 N)$ states per agent. We emphasize that our protocol can handle an adversary that can both insert and delete agents, a setting in which existing approximate counting techniques do not seem to apply. The protocol relies on a novel coloring strategy in which the population size is encoded in the variance of the distribution of colors. Individual agents can locally obtain a weak estimate of the population size by sampling from the distribution, and make individual decisions that robustly maintain a stable global population size