Space-Fluid Adaptive Sampling by Self-Organisation

TL;DR

Space-fluid adaptive sampling tackles decentralized sensing of spatially varying signals by introducing AggregateSampler, a self-stabilising, gradient-based region-growth algorithm within the aggregate computing framework. The method maps input fields to a regional partition that yields one sample per region, with region sizes controlled by a path-sampling-error bound $\eta$ and a symmetry-breaking efficiency $k$ ( proven to satisfy $k\ge 0.5$ ). Formal analysis and simulations (including PM$_{10}$ data) demonstrate self-stabilisation, local optimality, and a tunable trade-off between sampling accuracy and efficiency. This approach enables scalable, energy-aware spatial monitoring in large deployments with potential policy and environmental-sensing applications.

Abstract

A recurrent task in coordinated systems is managing (estimating, predicting, or controlling) signals that vary in space, such as distributed sensed data or computation outcomes. Especially in large-scale settings, the problem can be addressed through decentralised and situated computing systems: nodes can locally sense, process, and act upon signals, and coordinate with neighbours to implement collective strategies. Accordingly, in this work we devise distributed coordination strategies for the estimation of a spatial phenomenon through collaborative adaptive sampling. Our design is based on the idea of dynamically partitioning space into regions that compete and grow/shrink to provide accurate aggregate sampling. Such regions hence define a sort of virtualised space that is "fluid", since its structure adapts in response to pressure forces exerted by the underlying phenomenon. We provide an adaptive sampling algorithm in the field-based coordination framework, and prove it is self-stabilising and locally optimal. Finally, we verify by simulation that the proposed algorithm effectively carries out a spatially adaptive sampling while maintaining a tuneable trade-off between accuracy and efficiency.

Figures (16)

• Figure 1: Air quality statistics map taken from https://archive.ph/dMJO2. There are areas where the underlying phenomenon does not vary significantly in space (light-grey oval), hence sampling could be made sparser with tolerable loss of accuracy. In others (darker circle), variance is high, requiring a more detailed spatial sampling.
• Figure 2: Example of an event structure. In the node labels, superscripts denote device identifiers, while subscripts are progressive numbers denoting subsequent rounds at the same device. The blue (resp. green) background denotes the future (resp. past) of a reference event denoted with a yellow background.
• Figure 3: Example of a stabilising field. We use labels above the nodes to denote the values computed in the corresponding events, assuming the program is a gradient operator as per \ref{['example:gradient']}.
• Figure 4: Example of a regional partition field with regions $r_{blue}$, $r_{green}$, $r_{yellow}$, $r_{white}$ (the background is used to denote the output of the field). Notice that contiguity does not hold everywhere and anytime but only since event $\epsilon_2^3$.
• Figure 5: Example of a regional partitioning (with three contiguous regions) created by the algorithm on a simplified system where devices are arranged on a line. Notation: black dots denote the leaders/samplers; the coloured areas denote regions; and the red extension lines are used to denote the error-distances. Note that no device in a region can have path sampling error greater than $\eta/2$ with respect to the leader, and that very small regions can still exist in corner cases (e.g., the green region on the right).

Theorems & Definitions (22)

• Definition 3.1: Situated event structure
• Remark 3.2: Communication and distributed execution
• Definition 3.3: Computational field
• Definition 3.4: Field computation
• Definition 3.5: Field-based operator
• Example 3.6: Gradient field computation and operator
• Definition 3.7: Static environment
• Definition 3.8: Stabilising environment
• Definition 3.9: Stabilising field
• Definition 3.10: Stabilising computation