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- W20689310 abstract "Alice and Bob were excited about the bicycle tour they had long planned. They were going to ride during the day, carrying only light supplies, and stay in hotels at night. Alice had suggested they coordinate packing to avoid duplication and extra weight. Alice was to pack tools: a compass, spoke wrench, chain breaker, hub wrench, and spare tire tube; and Bob was to pack consumables: Water, toilet paper, sunscreen, trail mix, soap. They agreed that neither would pack more than c = 7 pounds of supplies. On the night before the trip Alice gathered everything on the kitchen table and prepared to pack; but it quickly became clear that she had staged rather more than 7 pounds. Decision time. Alice was a perfectionist. She realized the importance of packing the right stuff and so was prepared to think carefully about it. She methodically indexed the candidate items and listed the weight w i of each item i (Table 2.1 , 2nd row). But what to pack? Alice saw that she could fill the knapsack to the limit with items 1, 2, and 4. But then again she could just as well fill it with items 3 and 5 or with items 2, 4, and 5. Which is best? Or might it be better to pack only items 2 and 3 even if this alternative leaves some residual capacity unused? Why not pack only items 1 and 5 or only 3 and 4? Alice realized that each item would either be packed or left behind—2 choices, and so there were up to 2 5 = 32 possible ways to pack the knapsack. Not all of these are possible or even desirable, but it seemed as if she would have to consider each possibility explicitly and choose the best, whatever that meant. Alice saw that, to choose the best, she needed some way to distinguish the “value” of one packing from another. Was it better to pack the spoke wrench or the spare inner tube?" @default.
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- W20689310 date "2008-01-01" @default.
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- W20689310 title "The Knapsack Problem" @default.
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- W20689310 doi "https://doi.org/10.1007/978-0-387-73699-0_2" @default.
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