Optimal Algorithm for Online Multiple Knapsack Marcin Bie nkowski - PowerPoint PPT Presentation
Optimal Algorithm for Online Multiple Knapsack Marcin Bie nkowski Krzysztof Piecuch Maciej Pacut (speaker) Knapsack Knapsack Knapsack Knapsack Knapsack Knapsack Multiple Knapsack Textbook Knapsack (offline) Given one knapsack of
How many medium items should wait? 1 1 M M M L M M M M M M M M M M M M M M 1 1 too many waiting not enough waiting
How many medium items should wait? L L M M M M M
How many medium items should wait? L m L M M M M M Simplify: all mediums of size m ∈ (1 / 3 , 1 / 2]
How many medium items should wait? Answer: to have gain ≥ 0 . 59
How many medium items should wait? Each medium item is size m • gain on waiting = m • gain on stacked = 2 m M M • gain on large ≥ 1 − m L M M M M waiting
How many medium items should wait? Each medium item is size m M • gain on waiting = m • gain on stacked = 2 m M M • gain on large ≥ 1 − m L M M M M waiting
How many medium items should wait? Each medium item is size m • gain on waiting = m • gain on stacked = 2 m M M • gain on large ≥ 1 − m L M M M M waiting
How many medium items should wait? Each medium item is size m • gain on waiting = m • gain on stacked = 2 m M M • gain on large ≥ 1 − m L M M M M waiting
How many medium items should wait? Each medium item is size m M • gain on waiting = m • gain on stacked = 2 m M M • gain on large ≥ 1 − m L M M M M waiting
How many medium items should wait? Each medium item is size m • gain on waiting = m • gain on stacked = 2 m • gain on large ≥ 1 − m M M L M M M M waiting
How many medium items should wait? Each medium item is size m • gain on waiting = m • gain on stacked = 2 m • gain on large ≥ 1 − m M M L M M M M waiting
How many medium items should wait? Answer: fix m , solve for gain(#waiting) ≥ 0 . 59 0
How many medium items should wait? Answer: fix m , solve for gain(#waiting) ≥ 0 . 59 0
How many medium items should wait? Answer: fix m , solve for gain(#waiting) ≥ 0 . 59 0
How many medium items should wait? Answer: fix m , solve for gain(#waiting) ≥ 0 . 59 0
How many medium items should wait? Answer: fix m , solve for gain(#waiting) ≥ 0 . 59 0
How many medium items should wait? Answer: fix m , solve for gain(#waiting) ≥ 0 . 59 0
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