The clever shopper problem

Laurent Bulteau; Danny Hermelin; Anthony Labarre; Stéphane Vialette

doi:10.1007/978-3-319-90530-3_6

The clever shopper problem

Laurent Bulteau, Danny Hermelin, Anthony Labarre, Stéphane Vialette

Department of Industrial Engineering and Management

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-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 language	English
Title of host publication	Computer Science - Theory and Applications - 13th International Computer Science Symposium in Russia, CSR 2018, Proceedings
Editors	Vladimir V. Podolskii, Fedor V. Fomin
Publisher	Springer Verlag
Pages	53-64
Number of pages	12
ISBN (Print)	9783319905297
DOIs	https://doi.org/10.1007/978-3-319-90530-3_6
State	Published - 1 Jan 2018
Event	13th International Computer Science Symposium in Russia, CSR 2018 - Moscow, Russian Federation Duration: 6 Jun 2018 → 10 Jun 2018

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	10846 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	13th International Computer Science Symposium in Russia, CSR 2018
Country/Territory	Russian Federation
City	Moscow
Period	6/06/18 → 10/06/18

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

Access to Document

10.1007/978-3-319-90530-3_6

Cite this

Bulteau, L., Hermelin, D., Labarre, A., & Vialette, S. (2018). The clever shopper problem. In V. V. Podolskii, & F. V. Fomin (Eds.), Computer Science - Theory and Applications - 13th International Computer Science Symposium in Russia, CSR 2018, Proceedings (pp. 53-64). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10846 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-319-90530-3_6

Bulteau, Laurent ; Hermelin, Danny ; Labarre, Anthony et al. / The clever shopper problem. Computer Science - Theory and Applications - 13th International Computer Science Symposium in Russia, CSR 2018, Proceedings. editor / Vladimir V. Podolskii ; Fedor V. Fomin. Springer Verlag, 2018. pp. 53-64 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

@inproceedings{e0b57fe3768640e3ae9f31d30b5d85cf,

title = "The clever shopper problem",

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.",

author = "Laurent Bulteau and Danny Hermelin and Anthony Labarre and St{\'e}phane Vialette",

note = "Publisher Copyright: {\textcopyright} 2018, Springer International Publishing AG, part of Springer Nature.; 13th International Computer Science Symposium in Russia, CSR 2018 ; Conference date: 06-06-2018 Through 10-06-2018",

year = "2018",

month = jan,

day = "1",

doi = "10.1007/978-3-319-90530-3_6",

language = "English",

isbn = "9783319905297",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer Verlag",

pages = "53--64",

editor = "Podolskii, {Vladimir V.} and Fomin, {Fedor V.}",

booktitle = "Computer Science - Theory and Applications - 13th International Computer Science Symposium in Russia, CSR 2018, Proceedings",

address = "Germany",

}

Bulteau, L, Hermelin, D, Labarre, A & Vialette, S 2018, The clever shopper problem. in VV Podolskii & FV Fomin (eds), Computer Science - Theory and Applications - 13th International Computer Science Symposium in Russia, CSR 2018, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 10846 LNCS, Springer Verlag, pp. 53-64, 13th International Computer Science Symposium in Russia, CSR 2018, Moscow, Russian Federation, 6/06/18. https://doi.org/10.1007/978-3-319-90530-3_6

The clever shopper problem. / Bulteau, Laurent; Hermelin, Danny; Labarre, Anthony et al.
Computer Science - Theory and Applications - 13th International Computer Science Symposium in Russia, CSR 2018, Proceedings. ed. / Vladimir V. Podolskii; Fedor V. Fomin. Springer Verlag, 2018. p. 53-64 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10846 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - The clever shopper problem

AU - Bulteau, Laurent

AU - Hermelin, Danny

AU - Labarre, Anthony

AU - Vialette, Stéphane

PY - 2018/1/1

Y1 - 2018/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85048052225&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-90530-3_6

DO - 10.1007/978-3-319-90530-3_6

M3 - Conference contribution

AN - SCOPUS:85048052225

SN - 9783319905297

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 53

EP - 64

BT - Computer Science - Theory and Applications - 13th International Computer Science Symposium in Russia, CSR 2018, Proceedings

A2 - Podolskii, Vladimir V.

A2 - Fomin, Fedor V.

PB - Springer Verlag

T2 - 13th International Computer Science Symposium in Russia, CSR 2018

Y2 - 6 June 2018 through 10 June 2018

ER -

Bulteau L, Hermelin D, Labarre A, Vialette S. The clever shopper problem. In Podolskii VV, Fomin FV, editors, Computer Science - Theory and Applications - 13th International Computer Science Symposium in Russia, CSR 2018, Proceedings. Springer Verlag. 2018. p. 53-64. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-319-90530-3_6

The clever shopper problem

Abstract

Publication series

Conference

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this