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By Lemma 3, no two items in U could be combined in b. Since bn is smaller than b the same is clearly true of bn . Furthermore, each item in U is larger than e(b), so no item in U can be combined with yn in bn . Thus, to prove that FFDα will place yn in bn , we just need to prove that there is no item x ∈ U with |yn | < |x| ≤ |yn | + e(b). Assume for the sake of contradiction that such an item, x, exists. If |yn | ≥ 13 |b|, |x| + |yn | > 23 |b|, and this combination would be tried when packing b, unless an even better combination were found.

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A 2. 79 competitive online algorithm for two processor real-time systems with uniform value density by Qifan Y.

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