Randomized Strategies for Non-additive 3-Slope Ski Rental

Toni Böhnlein; Sapir Erlich; Zvi Lotker; Dror Rawitz

doi:10.1007/978-3-031-09993-9_4

Randomized Strategies for Non-additive 3-Slope Ski Rental

Toni Böhnlein, Sapir Erlich, Zvi Lotker, Dror Rawitz

Bar-Ilan University

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

Abstract

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 b_i and a rental rate r_i. 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 b_j- b_i ). 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.

Original language	English
Title of host publication	Structural Information and Communication Complexity - 29th International Colloquium, SIROCCO 2022, Proceedings
Editors	Merav Parter
Publisher	Springer Science and Business Media Deutschland GmbH
Pages	62-78
Number of pages	17
ISBN (Print)	9783031099922
DOIs	https://doi.org/10.1007/978-3-031-09993-9_4
State	Published - 1 Jan 2022
Event	29th International Colloquium on Structural Information and Communication Complexity, SIROCCO 2022 - Paderborn, Germany Duration: 27 Jun 2022 → 29 Jun 2022

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	13298 LNCS

Conference

Conference	29th International Colloquium on Structural Information and Communication Complexity, SIROCCO 2022
Country/Territory	Germany
City	Paderborn
Period	27/06/22 → 29/06/22

Keywords

Competitive analysis
Online algorithms
Randomized algorithm
Ski-rental

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
General Computer Science

Access to Document

10.1007/978-3-031-09993-9_4

Cite this

Böhnlein, T., Erlich, S., Lotker, Z., & Rawitz, D. (2022). Randomized Strategies for Non-additive 3-Slope Ski Rental. In M. Parter (Ed.), Structural Information and Communication Complexity - 29th International Colloquium, SIROCCO 2022, Proceedings (pp. 62-78). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 13298 LNCS). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-3-031-09993-9_4

Böhnlein, Toni ; Erlich, Sapir ; Lotker, Zvi et al. / Randomized Strategies for Non-additive 3-Slope Ski Rental. Structural Information and Communication Complexity - 29th International Colloquium, SIROCCO 2022, Proceedings. editor / Merav Parter. Springer Science and Business Media Deutschland GmbH, 2022. pp. 62-78 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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abstract = "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.",

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Böhnlein, T, Erlich, S, Lotker, Z & Rawitz, D 2022, Randomized Strategies for Non-additive 3-Slope Ski Rental. in M Parter (ed.), Structural Information and Communication Complexity - 29th International Colloquium, SIROCCO 2022, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 13298 LNCS, Springer Science and Business Media Deutschland GmbH, pp. 62-78, 29th International Colloquium on Structural Information and Communication Complexity, SIROCCO 2022, Paderborn, Germany, 27/06/22. https://doi.org/10.1007/978-3-031-09993-9_4

Randomized Strategies for Non-additive 3-Slope Ski Rental. / Böhnlein, Toni; Erlich, Sapir; Lotker, Zvi et al.
Structural Information and Communication Complexity - 29th International Colloquium, SIROCCO 2022, Proceedings. ed. / Merav Parter. Springer Science and Business Media Deutschland GmbH, 2022. p. 62-78 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 13298 LNCS).

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

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AU - Lotker, Zvi

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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.

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Böhnlein T, Erlich S, Lotker Z , Rawitz D. Randomized Strategies for Non-additive 3-Slope Ski Rental. In Parter M, editor, Structural Information and Communication Complexity - 29th International Colloquium, SIROCCO 2022, Proceedings. Springer Science and Business Media Deutschland GmbH. 2022. p. 62-78. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-031-09993-9_4

Randomized Strategies for Non-additive 3-Slope Ski Rental

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