All algorithms regarding asynchronous push/pull gossip (APPG) I can find are either on spreading a single piece of information, or on data aggregation like average sums.
I'm looking for an APPG algorithm in the following scenario:
Suppose we have a network of machines $G(t)$, and a set $S(t)$ of information, such that each member $g\in G(t)$ holds a subset of $S_i(t) \subset S(t)$. These sets might change over time. The goal is to use APPG, to approximate $S(t)$ by $S_i(t)$ for all members.
$S(t)$ can grow over time (but not shrink), by members extending their subsets $S_i(t)$, so the algorithm might continue forever, with the goal to get each $S_i(t)$ always as close to $S(t)$ as possible, while $S(t)$ grows.
The problem here is, that I don't really know how to search for the appropriate research papers. Its not data aggregation as far as I can see, nor is it really state or data-set replication. Its data set aggregation, IMO, but I can not find anything useful.
Maybe someone can also expand the tags a bit.