TY - GEN

T1 - Approximation and competitive algorithms for single-minded selling problem

AU - Chin, Francis Y.L.

AU - Poon, Sheung Hung

AU - Ting, Hing Fung

AU - Xu, Dachuan

AU - Yu, Dongxiao

AU - Zhang, Yong

N1 - Publisher Copyright:
© Springer Nature Switzerland AG 2018.

PY - 2018

Y1 - 2018

N2 - The problem of item selling with the objective of maximizing the revenue is studied. Given a seller with k types of items and n single-minded buyers, i.e., each buyer is only interested in a particular bundle of items, to maximize the revenue, the seller must carefully assign some amount of bundles to each buyer with respect to the buyer’s accepted price. Each buyer bi is associated with a value function vi(·) such that v i (x) is the accepted unit bundle price bi is willing to pay for x bundles. We show that the single-minded item selling problem is NP-hard. Moreover, we give an O(√k)-approximation algorithm. For the online version, i.e., the buyers come one by one and the decision on each buyer must be made before the arrival of the next buyer, an O(√k · (log h + log k))- competitive algorithm is achieved, where h is the highest unit item price among all buyers.

AB - The problem of item selling with the objective of maximizing the revenue is studied. Given a seller with k types of items and n single-minded buyers, i.e., each buyer is only interested in a particular bundle of items, to maximize the revenue, the seller must carefully assign some amount of bundles to each buyer with respect to the buyer’s accepted price. Each buyer bi is associated with a value function vi(·) such that v i (x) is the accepted unit bundle price bi is willing to pay for x bundles. We show that the single-minded item selling problem is NP-hard. Moreover, we give an O(√k)-approximation algorithm. For the online version, i.e., the buyers come one by one and the decision on each buyer must be made before the arrival of the next buyer, an O(√k · (log h + log k))- competitive algorithm is achieved, where h is the highest unit item price among all buyers.

UR - http://www.scopus.com/inward/record.url?scp=85058456353&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-04618-7_9

DO - 10.1007/978-3-030-04618-7_9

M3 - Conference contribution

AN - SCOPUS:85058456353

SN - 9783030046170

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

SP - 98

EP - 110

BT - Algorithmic Aspects in Information and Management - 12th International Conference, AAIM 2018, Proceedings

A2 - Butenko, Sergiy

A2 - Tang, Shaojie

A2 - Du, Ding-Zhu

A2 - Woodruff, David

PB - Springer Verlag

T2 - 12th International Conference on Algorithmic Aspects in Information and Management, AAIM 2018

Y2 - 3 December 2018 through 4 December 2018

ER -