Beating the Harmonic Lower Bound for Online Bin Packing

Rob Van Stee

17th March 2016, 10:00 in ADR LG26

In the online bin packing problem, items of sizes in $(0,1]$ arrive online to be packed into bins of size 1. The goal is to minimize the number of used bins.
In this paper, we present an online bin packing algorithm with asymptotic performance ratio of 1.5815, which constitutes the first improvement over the algorithm Harmonic++ in fifteen years and reduces the gap to the lower bound by roughly 15%. This algorithm achieved a competitive ratio of 1.58889 and is one instance of the Super Harmonic framework; a lower bound of Ramanan et al. shows that within this framework, no competitive ratio below 1.58333 can be achieved. We also give a lower bound of 1.5766 for variations of our algorithm.

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