Unit Cost Buyback Problem
Unit Cost Buyback Problem
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单位成本回购问题
DOI:
10.1007/s00224-018-9897-7
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发表时间:
2018-11
影响因子:
0.5
通讯作者:
Makino Kazuhisa
中科院分区:
文献类型:
--
作者:
Kawase Yasushi;Han Xin;Makino Kazuhisa
In this paper, we study theunit cost buyback problem, i.e., the buyback problem with a fixed cancellation cost for each canceled element. The input of the problem is a sequence of elementse1,e2, . . . ,enwhere each elementeihas a weightw(ei). We assume that the weights are in a known range [l,u], i.e.,l≤w(ei) ≤ufor anyi. Given theith elementei, we either accepteior reject it with no cost, where we can keep a set of elements that satisfies a certain constraint. In order to accept a new elementei, we can cancel some previously selected elements at a cost which is proportional to the number of elements canceled. Our goal is to maximize the profit, i.e., the total weights of elements accepted (and not canceled) minus the total cancellation cost occurred. We construct optimal online algorithms and prove that they are the best possible when the constraint is a matroid constraint or the unweighted knapsack constraint.
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