Lower Bounds for Several Online Variants of Bin Packing
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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.
KeywordsBin packing Online algorithms Lower bounds Competitive ratio
An extended abstract version appears in the Proceedings of WAOA2017. J. Balogh was supported by the project “Integrated program for training new generation of scientists in the fields of computer science”, no. EFOP-3.6.3-VEKOP-16-2017-0002. J. Békési was supported by the EU-funded Hungarian grant EFOP-3.6.2-16-2017-00015. Gy. Dósa was supported by Szechenyi 2020 under the EFOP-3.6.1-16-2016-00015 and by National Research, Development and Innovation Office NKFIH under the grant SNN 116095. L. Epstein and A. Levin were partially supported by a grant from GIF - the German-Israeli Foundation for Scientific Research and Development (grant number I-1366-407.6/2016).
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