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The Clever Shopper Problem

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Computer Science – Theory and Applications (CSR 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10846))

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Abstract

We investigate a variant of the so-called Internet Shopping problem introduced by Blazewicz et al. (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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Author information

Authors and Affiliations

  1. Université Paris-Est, LIGM (UMR 8049), CNRS, ENPC, ESIEE Paris, UPEM, 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

Authors
  1. Laurent Bulteau
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  2. Danny Hermelin
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  3. Anthony Labarre
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  4. Stéphane Vialette
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Corresponding author

Correspondence to Anthony Labarre .

Editor information

Editors and Affiliations

  1. Department of Informatics, University of Bergen, Bergen, Norway

    Fedor V. Fomin

  2. Steklov Mathematical Institute, Moscow, Russia

    Vladimir V. Podolskii

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Bulteau, L., Hermelin, D., Labarre, A., Vialette, S. (2018). The Clever Shopper Problem. In: Fomin, F., Podolskii, V. (eds) Computer Science – Theory and Applications. CSR 2018. Lecture Notes in Computer Science(), vol 10846. Springer, Cham. https://doi.org/10.1007/978-3-319-90530-3_6

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  • DOI: https://doi.org/10.1007/978-3-319-90530-3_6

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-90529-7

  • Online ISBN: 978-3-319-90530-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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