More on online cardinality constrained bin packing with small cardinality bounds

We revisit online bin packing with cardinality constraints. In this problem, a set of items of positive sizes not larger than 1 and an integer parameter k ≥ 2 are given. The goal is to partition the items into the minimum number of valid bins, where a valid bin is a set of at most k items whose total size is at most 1. We provide better bounds on the asymptotic competitive ratio for cardinality constrained bin packing for k=3, showcasing current methods for designing algorithms for bin packing problems. We extend the lower bound construction for k=3 for other values of k, improving all known lower bounds on the best possible asymptotic competitive ratio for small k ≥ 3.