The Clever Shopper Problem

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

doi:10.1007/s00224-019-09917-z

The Clever Shopper Problem

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

Department of Industrial Engineering and Management

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

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.

Original language	English
Pages (from-to)	17-34
Number of pages	18
Journal	Theory of Computing Systems
Volume	64
Issue number	1
DOIs	https://doi.org/10.1007/s00224-019-09917-z
State	Published - 1 Jan 2020

Keywords

Clever shopper
Fixed parameter tractability
Internet shopping

ASJC Scopus subject areas

Theoretical Computer Science
Computational Theory and Mathematics

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10.1007/s00224-019-09917-z

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The Clever Shopper Problem

Abstract

Keywords

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