Computing cores

The heuristics we describe in this section compute Core$(h)$ in time linear with the number of attributes in $h.apps$. These heuristics reference the set $\cal C$ of containers and the three functions $m_c, m_s$ and $m_h$, but they do not reference the full set $\cal A$ of attributes. In addition, these heuristics do not enumerate $\cal H$, but they do reference the configuration of hosts (to reference the configuration of a host $h^\prime$, they reference $h^\prime.os$ and $h^\prime.apps$). Thus, the container/sub-container hierarchy is the only data structure that the heuristics use to compute cores.