Bin covering is a dual version of classic bin packing. Thus, the goal is to
cover as many bins as possible, where covering a bin means packing items of
total size at least one in the bin.
For online bin covering, competitive analysis fails to distinguish between
most algorithms of interest; all "reasonable" algorithms have a competitive
ratio of 1/2. Thus, in order to get a better understanding of the combinatorial
difficulties in solving this problem, we turn to other performance measures,
namely relative worst order, random order, and max/max analysis, as well as
analyzing input with restricted or uniformly distributed item sizes. In this
way, our study also supplements the ongoing systematic studies of the relative
strengths of various performance measures.
Two classic algorithms for online bin packing that have natural dual versions
are Harmonic and Next-Fit. Even though the algorithms are quite different in
nature, the dual versions are not separated by competitive analysis. We make
the case that when guarantees are needed, even under restricted input
sequences, dual Harmonic is preferable. In addition, we establish quite robust
theoretical results showing that if items come from a uniform distribution or
even if just the ordering of items is uniformly random, then dual Next-Fit is
the right choice.Comment: IMADA-preprint-c