  We consider (closed neighbourhood) packings and their generalization in
graphs called limited packings. A vertex set X in a graph G is a k-limited
packing if for any vertex $v\in V(G)$, $\left|N[v] \cap X\right| \le k$, where
$N[v]$ is the closed neighbourhood of $v$. The k-limited packing number
$L_k(G)$ is the largest size of a k-limited packing in G. Limited packing
problems can be considered as secure facility location problems in networks. We
develop probabilistic and greedy approaches to limited packings in graphs,
providing lower bounds for the k-limited packing number, and randomized and
greedy algorithms to find k-limited packings satisfying the bounds. Some upper
bounds for $L_k(G)$ are given as well. The problem of finding a maximum size
k-limited packing is known to be NP-complete even in split or bipartite graphs.
