ISAAC 2013: Algorithms and Computation pp 435-445

• Yasushi Kawase
• Xin Han
• Kazuhisa Makino
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8283)

## Abstract

In this paper, we study unit cost buyback problem, i.e., the buyback problem with fixed cancellation cost for each cancelled item. The input is a sequence of elements e 1,e 2,…,e n , each of which has a weight w(e i ). We assume that weights have an upper and a lower bound, i.e., l ≤ w(e i ) ≤ u for any i. Given the ith element e i , we either accept e i or reject it with no cost, subject to some constraint on the set of accepted elements. In order to accept a new element e i , we could cancel some previous selected elements at a cost which is proportional to the number of elements canceled. Our goal is to maximize the profit, i.e., the sum of the 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.

## Keywords

Knapsack Problem Competitive Ratio Online Algorithm Competitive Algorithm Knapsack Constraint
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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## Authors and Affiliations

• Yasushi Kawase
• 1
• Xin Han
• 2
• Kazuhisa Makino
• 3
1. 1.University of TokyoJapan
2. 2.Dalian University of TechnologyChina
3. 3.Kyoto UniversityJapan