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 than "k" of the subsets, the answer can be approximated within a factor of "k". This is also true for the weighted version. There is a one-to-one polynomial-time reduction between the independent set problem and the set packing problem: This is also a bidirectional PTAS reduction, and it shows that the two problems are equally difficult to approximate. Matching and 3-dimensional matching are special cases of set packing. A maximum-size matching can be found in polynomial time, but finding a largest 3-dimensional matching or a largest independent set is NP-hard. Set packing is one among a family of problems related