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Bin packing: Given a set of $k$ items where item $j$ has size $s_j$ and a set of bins of capacity $C$ each. Use the minimum number of bins to pack all items while respecting the capacity of the used bins.

If I select one bin arbitrarily and put in it the maximum possible number of items and repeat this until no item is left. Why I won't get a logarithmic factor approximation algorithm as in set covet problem?

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