The share Operator for Field-Based Coordination

Abstract

Recent work in the area of coordination models and collective adaptive systems promotes a view of distributed computations as functions manipulating computational fields (data structures spread over space and evolving over time), and introduces the field calculus as a formal foundation for field computations. With the field calculus, evolution (time) and neighbor interaction (space) are handled by separate functional operators: however, this intrinsically limits the speed of information propagation that can be achieved by their combined use. In this paper, we propose a new field-based coordination operator called share, which captures the space-time nature of field computations in a single operator that declaratively achieves: (i) observation of neighbors' values; (ii) reduction to a single local value; and (iii) update and converse sharing to neighbors of a local variable. In addition to conceptual economy, use of the share operator also allows many prior field calculus algorithms to be greatly accelerated, which we validate empirically with simulations of a number of frequently used network propagation and collection algorithms.

From distributed coordination to field calculus and aggregate computing

“…Early work in this area [131] shows that the field calculus is a promising language for expressing runtime properties to be monitored (which may in turn be expressed either in field calculus or in other formalisms). The recent development of the share construct for optimal state diffusion [132] further supports this claim, by providing means to check temporal properties without delays. Notably, runtime verification methods are often too expensive to be used on the complex state spaces of distributed systems, leading to the development of state-reduction methods like mean-field approximation [133,134]; field calculus may provide an alternative method for state reduction that is more readily able to be applied to a broader class of systems.…”

Addressing Collective Computations Efficiency: Towards a Platform-level Reinforcement Learning Approach

“…To prove that Bounded Election is selfstabilising, we show that it is an instance of the minimising share pattern, which is proved in [43], following the framework of [36], that it is self-stabilising. We do so by rewriting the minimising share, preserving self-stabilisation, until we obtain an algorithm that is functionally equivalent to to Algorithm 1.…”

“…2) The minimising share pattern: In [43], it is proved that an expression of the following form is self-stabilising:…”

Aggregate Processes as Distributed Adaptive Services for the Industrial Internet of Things

“…• nbr(CALL, v 0 , f ) (whose logic is described in [2] as the share operator), computes the result of applying f to the neighbouring field of values of the whole nbr function at the previous computation cycle of neighbour nodes (using v 0 for the current node if no such value is available).…”