Effect of Monotonic Filtering on Graph Collection Dynamics

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 of aggregates 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 $2N$ .