租、租或买：多坡度滑雪板租赁的随机算法
Rent, Lease or Buy: Randomized Algorithms for Multislope Ski Rental
摘要：
在多斜坡滑雪租赁问题中，用户需要在某个未知的时间段内使用某个资源。要使用资源，用户必须订阅几个选项之一，每个选项包括一次性设置成本（"购买价格“）和与使用时间成比例的成本（"租赁费率”）。价格越高，租金越低。实际使用时间由对手决定，算法的目标是通过在任何时间点选择最佳选项来最小化成本。多斜坡滑雪租赁是经典滑雪租赁问题（其中唯一的选项是纯租和纯买）的自然推广，这是在线计算的基本问题之一。多坡度滑雪租赁问题是许多问题的抽象，其中在线决策不能仅由两个选项建模，例如，可以部分关闭的系统中的电源管理。本文研究了多坡度滑雪板租赁的随机算法。我们的研究结果包括最好的在线随机化策略的任何添加剂的情况下，从一个选项切换到另一个选项的成本是在他们的购买价格的差异;和算法，产生一个$e$竞争的随机化策略的任何（非添加剂）的实例。
英文摘要：
In the Multislope Ski Rental problem, the user needs a certain resource for some unknown period of time. To use the resource, the user must subscribe to one of several options, each of which consists of a one-time setup cost (``buying price''), and cost proportional to the duration of the usage (``rental rate''). The larger the price, the smaller the rent. The actual usage time is determined by an adversary, and the goal of an algorithm is to minimize the cost by choosing the best option at any point in time. Multislope Ski Rental is a natural generalization of the classical Ski Rental problem (where the only options are pure rent and pure buy), which is one of the fundamental problems of online computation. The Multislope Ski Rental problem is an abstraction of many problems where online decisions cannot be modeled by just two options, e.g., power management in systems which can be shut down in parts. In this paper we study randomized algorithms for Multislope Ski Rental. Our results include the best possible online randomized strategy for any additive instance, where the cost of switching from one option to another is the difference in their buying prices; and an algorithm that produces an $e$-competitive randomized strategy for any (non-additive) instance.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
