Dynamic Pricing Algorithms for Online Set Cover
Max Bender, Aum Desai, Jialin He, Oliver Thompson, Pramithas Upreti
TL;DR
This work studies Online Set Cover under a dynamic pricing framework where the server prices its controlled resources and clients choose the cheapest covering option. It proves that an exact equivalence exists between monotone OSC algorithms and priceable ones, via the PathPrice construction, and identifies a strongly competitive deterministic algorithm parameterized by the input frequency $f$. The central result is a $\\Theta(f)$-competitive dynamic pricing algorithm, optimal for deterministic strategies, achieved by transforming a monotone Primal-Dual by Frequency algorithm into a pricing scheme. The findings bridge dynamic pricing and OSC, establishing both upper and matching lower bounds, and highlight directions for extending to randomized settings and other parameter regimes.
Abstract
We consider dynamic pricing algorithms as applied to the online set cover problem. In the dynamic pricing framework, we assume the standard client server model with the additional constraint that the server can only place prices over the resources they maintain, rather than authoritatively assign them. In response, incoming clients choose the resource which minimizes their disutility when taking into account these additional prices. Our main contributions are the categorization of online algorithms which can be mimicked via dynamic pricing algorithms and the identification of a strongly competitive deterministic algorithm with respect to the frequency parameter of the online set cover input.