A tight lower bound for the online bounded space hypercube bin packing problem
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In the d-dimensional hypercube bin packing problem, a given list of d-dimensional hypercubes must be packed into the smallest number of hypercube bins. Epstein and van Stee [SIAM J. Comput. 35 (2005)] showed that the asymptotic performance ratio ρ of the online bounded space variant is Ω(log d) and O(d/log d), and conjectured that it is Θ(log d). We show that ρ is in fact Θ(d/log d), using probabilistic arguments.
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