# Field-based Coordination with the Share Operator

arXiv: https://arxiv.org/abs/1910.02874 · HTML: https://mlsanity.com/paper/1910.02874/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Oct 2019.

## Built on by (most cited first, 2 of 2)

- [FBFL: A Field-Based Coordination Approach for Data Heterogeneity in Federated Learning](https://mlsanity.com/paper/2502.08577/) (2025)
- [Space-Fluid Adaptive Sampling by Self-Organisation](https://mlsanity.com/paper/2210.17505/) (2022)

## Abstract (arXiv)

Field-based coordination has been proposed as a model for coordinating collective adaptive systems, promoting a view of distributed computations as functions manipulating data structures spread over space and evolving over time, called computational fields. The field calculus is a formal foundation for field computations, providing specific constructs for evolution (time) and neighbor interaction (space), which are handled by separate operators (called rep and nbr, respectively). This approach, however, 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. We show that for an important class of self-stabilising computations, share can replace all occurrences of rep and nbr constructs. 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 frequently used network propagation and collection algorithms.