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- W289158701 abstract "The bin packing problem is to find the minimum number of bins of size one to pack a list of items with sizes $a_1,..., a_n$ in $(0,1]$. Using uniform sampling, which selects a random element from the input list each time, we develop a randomized $O({n(log n)(loglog n)over sum_{i=1}^n a_i}+({1over epsilon})^{O({1overepsilon})})$ time $(1+epsilon)$-approximation scheme for the bin packing problem. We show that every randomized algorithm with uniform random sampling needs $Omega({nover sum_{i=1}^n a_i})$ time to give an $(1+epsilon)$-approximation. For each function $s(n): Nrightarrow N$, define $sum(s(n))$ to be the set of all bin packing problems with the sum of item sizes equal to $s(n)$. For a constant $bin (0,1)$, every problem in $sum(n^{b})$ has an $O(n^{1-b}(log n)(loglog n)+({1over epsilon})^{O({1overepsilon})})$ time $(1+epsilon)$-approximation for an arbitrary constant $epsilon$. On the other hand, there is no $o(n^{1-b})$ time $(1+epsilon)$-approximation scheme for the bin packing problems in $sum(n^{b})$ for some constant $epsilon>0$." @default.
- W289158701 created "2016-06-24" @default.
- W289158701 creator A5050029957 @default.
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- W289158701 date "2010-07-07" @default.
- W289158701 modified "2023-09-23" @default.
- W289158701 title "A Dense Hierarchy of Sublinear Time Approximation Schemes for Bin Packing" @default.
- W289158701 doi "https://doi.org/10.48550/arxiv.1007.1260" @default.
- W289158701 hasPublicationYear "2010" @default.
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