set of helpers for the latest newcomer. The function $D_\tau(\cdot)$ can be designed independently for each time slot $\tau=1,2,\cdots$. One can see that the DHS schemes are the most general form of helper selection.

A sub-class of the DHS schemes is the set of *stationary helper selection (SHS)* schemes that assign fixed helper sets of $d$ nodes to each node. The idea is that, for a given node failure, the same helper set is used at any time instant and thus the name stationary. Mathematically, in SHS, each node $i$ is associated with a set of indices $D_i$ where the size of $D_i$ is $d$. Whenever node $i$ fails, the newcomer (for node $i$) simply accesses those helpers $u\in D_i$ and requests $\beta$ amount of data from each helper.

It is not hard to see that SHS is indeed a subset of DHS by observing that any SHS is a DHS with the helper set decision at time $\tau$ being $$\begin{aligned}
D_\tau(\{F_l\}_{l=1}^{\tau})=D_{i}~\text{if $F_\tau=i$}.\nonumber\end{aligned}$$ Also note that while DHS allows different $D_\tau(\cdot)$ for different $\tau$, the helper set collection $\{D_i:\text{all nodes i}\}$ of SHS is fixed.

Our FHS scheme described in Section \[subsec:desc\_fr\] is an example of a SHS scheme. Since 