Competitive Algorithms for an Online Rent or Buy Problem with Variable Demand

Abstract

We consider a generalization of the classical Ski Rental Problem motivated by applications in cloud computing. We develop deterministic and probabilistic online algorithms for rent/buy decision problems with time-varying demand. We show that these algorithms have competitive ratios of 2 and 1.582 respectively. We also further establish the optimality of these algorithms. 233

Interleaved Caching with Access Graphs

“…It is easy to cast the classical ski rental problem in this framework by setting x i = 1 for the first x days and to 0 later. Kodialam [15] considers this generalization and gives a deterministic algorithm with a competitive ratio of 2 as well as a randomized algorithm with competitive ratio of e e−1 . Now suppose we have predictions y i for the demand on day i.…”

Customizing ML Predictions for Online Algorithms

“…But, this is where the uncertainty lies: the length of use is often not known in advance. The ski rental problem is perhaps the most fundamental, and structurally simplest, of all problems in online algorithms, and has been widely studied in many contexts (see, e.g., [1,2,3,4,5]), including that of online algorithms with ML predictions [6,7]. We formally define this problem next.…”

“…It is well-known that the best competitive ratio achievable by a deterministic algorithm for this problem is 2 (e.g., [8]), and that by a randomized algorithm is e e−1 (e.g., [1]). The ski-rental problem [1,3,4,5], and variants such as TCP acknowledgment [2], the parking permit problem [9], snoopy caching [8], etc. model the fundamental difficulty in decision making under uncertainty in many situations.…”