2024/02/16 by Brustle, Johannes, Correa, José, Dütting, Paul +3
#60G40 #62L15 #68W27 #90C59 #Computer Science and Game Theory (cs.GT) #Data Structures and Algorithms (cs.DS) #FOS: Computer and information sciences
paper · doi:10.48550/arxiv.2402.11084
We study the classic single-choice prophet inequality problem through a resource augmentation lens. Our goal is to bound the (1-ε)-competition complexity of different types of online algorithms. This metric asks for the smallest k such that the expected value of the online algorithm on k copies of the original instance, is at least a (1-ε)-approximation to the expected offline optimum on a single copy. We show that block threshold algorithms, which set one threshold per copy, are optimal and give a tight bound of k = Θ(log log 1/ε). This shows that block threshold algorithms approach the offline optimum doubly-exponentially fast. For single threshold algorithms, we give a tight bound of k = Θ(log 1/ε), establishing an exponential gap between block threshold algorithms and single threshold algorithms. Our model and results pave the way for exploring resource-augmented prophet inequalities in combinatorial settings. In line with this, we present preliminary findings for bipartite matching with one-sided vertex arrivals, as well as in XOS combinatorial auctions. Our results have a natural competition complexity interpretation in mechanism design and pricing applications.