Monotonic Filtering for Distributed Collection

TL;DR

This paper analyzes monotonic filtering in distributed data collection networks, demonstrating it limits overestimates to at most twice the number of devices, regardless of network topology.

Contribution

It extends previous work by analyzing monotonic filtering's effectiveness in arbitrary network topologies, establishing a worst-case overestimate bound of 2N.

Findings

Monotonic filtering prevents large overestimates after source switches.

The maximum overestimate is bounded by 2N in any network topology.

The approach improves accuracy during transient phases in distributed data collection.

Abstract

Distributed data collection is a fundamental task in open systems. In such networks, data is aggregated across a network to produce a single aggregated result at a source device. Though self-stabilizing, algorithms performing data collection can produce large overestimates in the transient phase. For example, in [1] we demonstrated that in a line graph, a switch of sources after initial stabilization may produce overestimates that are quadratic in the network diameter. We also proposed monotonic filtering as a strategy for removing such large overestimates. Monotonic filtering prevents the transfer of data from device A to device B unless the distance estimate at A is more than that at B at the previous iteration. For a line graph, [1] shows that monotonic filtering prevents quadratic overestimates. This paper analyzes monotonic filtering for an arbitrary graph topology, showing that for an N device network, the largest overestimate after switching sources is at most 2N.