Randomized Strategies for Non-additive 3-Slope Ski Rental

Toni Böhnlein, Sapir Erlich, Zvi Lotker, Dror Rawitz

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


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.

Original languageEnglish
Title of host publicationStructural Information and Communication Complexity - 29th International Colloquium, SIROCCO 2022, Proceedings
EditorsMerav Parter
PublisherSpringer Science and Business Media Deutschland GmbH
Number of pages17
ISBN (Print)9783031099922
StatePublished - 1 Jan 2022
Externally publishedYes
Event29th International Colloquium on Structural Information and Communication Complexity, SIROCCO 2022 - Paderborn, Germany
Duration: 27 Jun 202229 Jun 2022

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume13298 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference29th International Colloquium on Structural Information and Communication Complexity, SIROCCO 2022


  • Competitive analysis
  • Online algorithms
  • Randomized algorithm
  • Ski-rental

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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