The Clever Shopper Problem

Laurent Bulteau, Dan Hermelin, Anthony Labarre, Stéphane Vialette

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

1 Scopus citations

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.

Original languageEnglish GB
Title of host publicationComputer Science – Theory and Applications
Subtitle of host publication13th International Computer Science Symposium in Russia, CSR 2018
EditorsFedor V. Fomin, Vladimir V. Podolskii
PublisherSpringer
Pages53-64
Number of pages12
ISBN (Print)9783319905297
DOIs
StatePublished - 1 Jan 2018
Event13th International Computer Science Symposium in Russia, CSR 2018 - Moscow, Russian Federation
Duration: 6 Jun 201810 Jun 2018

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
PublisherSpringer Verlag
Volume10846
ISSN (Print)0302-9743

Conference

Conference13th International Computer Science Symposium in Russia, CSR 2018
Country/TerritoryRussian Federation
CityMoscow
Period6/06/1810/06/18

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science (all)

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