TY - GEN
T1 - Randomized Strategies for Non-additive 3-Slope Ski Rental
AU - Böhnlein, Toni
AU - Erlich, Sapir
AU - Lotker, Zvi
AU - Rawitz, Dror
N1 - Publisher Copyright:
© 2022, Springer Nature Switzerland AG.
PY - 2022/1/1
Y1 - 2022/1/1
N2 - The Ski Rental problem captures the dilemma of choosing between renting and buying, and it is one of the fundamental problems in online computation. In many realistic scenarios there may be several intermediate lease options which are modelled by the Multi-Slope Ski Rental problem. An instance consists of k states where each state i∈ {0, …, k- 1 } is characterized by a buying cost bi and a rental rate ri. Previous work on instance-dependent strategies for Multi-Slope Ski Rental dealt with deterministic strategies or strategies for additive instances (instance where going from state i to state j costs bj- bi ). However, obtaining instance-dependent randomized strategies for non-additive instances remains open. In this paper, we advance towards answering this open question by characterizing optimal randomized strategies in the non-additive case, and providing an algorithm that computes near-optimal instance-dependent randomized strategies for Multi-Slope Ski Rental with three slopes (k= 2 ). The algorithm uses parametric search and a decision algorithm which is based on the characterization of optimal randomized strategies.
AB - The Ski Rental problem captures the dilemma of choosing between renting and buying, and it is one of the fundamental problems in online computation. In many realistic scenarios there may be several intermediate lease options which are modelled by the Multi-Slope Ski Rental problem. An instance consists of k states where each state i∈ {0, …, k- 1 } is characterized by a buying cost bi and a rental rate ri. Previous work on instance-dependent strategies for Multi-Slope Ski Rental dealt with deterministic strategies or strategies for additive instances (instance where going from state i to state j costs bj- bi ). However, obtaining instance-dependent randomized strategies for non-additive instances remains open. In this paper, we advance towards answering this open question by characterizing optimal randomized strategies in the non-additive case, and providing an algorithm that computes near-optimal instance-dependent randomized strategies for Multi-Slope Ski Rental with three slopes (k= 2 ). The algorithm uses parametric search and a decision algorithm which is based on the characterization of optimal randomized strategies.
KW - Competitive analysis
KW - Online algorithms
KW - Randomized algorithm
KW - Ski-rental
UR - http://www.scopus.com/inward/record.url?scp=85134312382&partnerID=8YFLogxK
U2 - 10.1007/978-3-031-09993-9_4
DO - 10.1007/978-3-031-09993-9_4
M3 - Conference contribution
AN - SCOPUS:85134312382
SN - 9783031099922
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 62
EP - 78
BT - Structural Information and Communication Complexity - 29th International Colloquium, SIROCCO 2022, Proceedings
A2 - Parter, Merav
PB - Springer Science and Business Media Deutschland GmbH
T2 - 29th International Colloquium on Structural Information and Communication Complexity, SIROCCO 2022
Y2 - 27 June 2022 through 29 June 2022
ER -