TY - GEN

T1 - The Clever Shopper Problem

AU - Bulteau, Laurent

AU - Hermelin, Dan

AU - Labarre, Anthony

AU - Vialette, Stéphane

N1 - Publisher Copyright:
© 2018, Springer International Publishing AG, part of Springer Nature.

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

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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

A2 - Fomin, Fedor V.

A2 - Podolskii, Vladimir V.

PB - Springer

Y2 - 6 June 2018 through 10 June 2018

ER -