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- W3046452434 abstract "We consider the online vector bin packing problem where $n$ items specified by $d$-dimensional vectors must be packed in the fewest number of identical $d$-dimensional bins. Azar et al. (STOC'13) showed that for any online algorithm $A$, there exist instances I, such that $A(I)$, the number of bins used by $A$ to pack $I$, is $Omega(d/log^2 d)$ times $OPT(I)$, the minimal number of bins to pack $I$. However in those instances, $OPT(I)$ was only $O(log d)$, which left open the possibility of improved algorithms with better asymptotic competitive ratio when $OPT(I) gg d$. We rule this out by showing that for any arbitrary function $q(cdot)$ and any randomized online algorithm $A$, there exist instances $I$ such that $ E[A(I)] geq ccdot d/log^3d cdot OPT(I) + q(d)$, for some universal constant $c$." @default.
- W3046452434 created "2020-08-07" @default.
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- W3046452434 date "2020-07-30" @default.
- W3046452434 modified "2023-09-27" @default.
- W3046452434 title "An Asymptotic Lower Bound for Online Vector Bin Packing" @default.
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