Several methods of analysis for cardinality constrained bin packing

We consider a known variant of bin packing called cardinality constrained packing, also with constraints (BPCC). In this problem, there is parameter k≥2, and items rational sizes in [0,1] are to be packed into bins, such that no has more than k or total size larger 1. The goal minimize the number bins. A recently introduced concept, price clustering, deals inputs presented way they split clusters. Thus, an item two attributes which its cluster. measure relation between optimal solution cannot combine different clusters can arbitrarily. Usually may large, while relatively small, though not trivially small. Such problems related greedy algorithms, batched similar but constant large analyze clustering for BPCC, including parametric case bounded sizes. discuss several algorithms problem were studied past, comment on packing.