Online Generalized Network Design Under (Dis)Economies of Scale

Abstract

We consider a general online network design problem in which a sequence of N requests arrive over time, each of which needs to use some subset of the available resources E. The cost incurred by a resource [Formula: see text] is some function fe of the total load [Formula: see text] on that resource. The objective is to minimize the total cost [Formula: see text]. We focus on cost functions that exhibit (dis)economies of scale. These functions are of the form [Formula: see text] if x > 0 (and zero if x = 0), in which the exponent [Formula: see text]. Optimization problems under these functions have received significant recent attention because of applications in energy-efficient computing. Our main result is a deterministic online algorithm with tight competitive ratio [Formula: see text] when αe is constant for all [Formula: see text]. This framework is applicable to a variety of network design problems in undirected and directed graphs, including multicommodity routing, Steiner tree/forest connectivity, and set connectivity. In fact, our online competitive ratio even matches the previous best (offline) approximation ratio. We also demonstrate the practical performance of our online algorithm on instances of multicommodity routing. Funding: This work was supported by the Directorate for Computer and Information Science and Engineering [Grant CCF-1750127] and the Division of Civil, Mechanical and Manufacturing Innovation [Grant CMMI-1940766].