The Clever Shopper Problem

Laurent Bulteau, Danny Hermelin, Dušan Knop, Anthony Labarre, Stéphane Vialette

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


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.

Original languageEnglish
Pages (from-to)17-34
Number of pages18
JournalTheory of Computing Systems
Issue number1
StatePublished - 1 Jan 2020


  • Clever shopper
  • Fixed parameter tractability
  • Internet shopping

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computational Theory and Mathematics


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