Lower bounds for several online variants of bin packing
J\'anos Balogh, J\'ozsef B\'ek\'esi, Gy\"orgy D\'osa, Leah Epstein,, Asaf Levin
TL;DR
This paper establishes new lower bounds on the competitive ratios for various online bin packing variants, notably improving the known bounds for online square packing from about 1.68 to over 1.75.
Contribution
It introduces a method of fully adaptive constructions to derive tighter lower bounds for online bin packing problems.
Findings
Lower bound for online square packing increased to above 1.75
Improved lower bounds for several online bin packing variants
Method of fully adaptive constructions developed
Abstract
We consider several previously studied online variants of bin packing and prove new and improved lower bounds on the asymptotic competitive ratios for them. For that, we use a method of fully adaptive constructions. In particular, we improve the lower bound for the asymptotic competitive ratio of online square packing significantly, raising it from roughly 1.68 to above 1.75.
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