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The Clever Shopper Problem

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Abstract

We investigate a variant of the so-called Internet Shopping problem introduced by Blazewicz et al. (Appl. Math. Comput. Sci. 20, 385–390, 2010), where a customer wants to buy a list of products at the lowest possible total cost from shops which offer discounts when purchases exceed a certain threshold. Although the problem is NP-hard, we provide exact algorithms for several cases, e.g. when each shop sells only two items, and an FPT algorithm for the number of items, or for the number of shops when all prices are equal. We complement each result with hardness proofs in order to draw a tight boundary between tractable and intractable cases. Finally, we give an approximation algorithm and hardness results for the problem of maximising the sum of discounts

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Authors and Affiliations

  1. Université Paris-Est, LIGM (UMR 8049), CNRS, ENPC, ESIEE Paris, UPEM, F-77454, Marne-la-Vallée, France

    Laurent Bulteau, Anthony Labarre & Stéphane Vialette

  2. Department of Industrial Engineering and Management, Ben-Gurion University of the Negev, Beersheba, Israel

    Danny Hermelin

  3. Department of Theoretical Computer Science, Faculty of Information Technology, Czech Technical University in Prague, Prague, Czech Republic

    Dušan Knop

Authors
  1. Laurent Bulteau
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  2. Danny Hermelin
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  3. Dušan Knop
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  4. Anthony Labarre
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  5. Stéphane Vialette
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Correspondence to Anthony Labarre.

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This article is part of the Topical Collection on Computer Science Symposium in Russia (2018)

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Bulteau, L., Hermelin, D., Knop, D. et al. The Clever Shopper Problem. Theory Comput Syst 64, 17–34 (2020). https://doi.org/10.1007/s00224-019-09917-z

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