Random close pack crystal lattices have maximum densities equal to this upper limit. Random close packing does not have a precise geometric definition. It is defined statistically, and results are empirical. A container is randomly filled with objects, and then the container is shaken or tapped until the objects do not compact any further, at this point the packing state is RCP. The definition of packing fraction can be given as: "the volume taken by number of particles in a given space of volume". In other words, packing fraction defines the packing density. It has been shown that the filling fraction increases with
Set packing example, we can use a greedy algorithm where we look for the set which intersects the smallest number of other sets, add it to our solution, and remove the sets it intersects. We continually do this until no sets are left, and we have a set packing of some size, although it may not be the maximum set packing. Although no algorithm can always produce results close to the maximum (see next section), on many practical inputs these heuristics do so. The set packing problem is not only NP-complete, but its optimization version (general maximum set packing problem) has been