# Title: An online algorithm for maximizing submodular functions,

# Authors: M. Streeter and D. Golovin

# Abstract

We present an algorithm for solving a broad class of online resource allocation problems. Our online algorithm can be applied in environments where abstract jobs arrive one at a time, and one can complete the jobs by investing time in a number of abstract activities, according to some schedule. We assume that the fraction of jobs completed by a schedule is a monotone, submodular function of a set of pairs (v,τ), where τ is the time invested in activity v. Under this as- sumption, our online algorithm performs near-optimally according to two natural metrics: (i) the fraction of jobs completed within time T, for some fixed dead- line T > 0, and (ii) the average time required to complete each job. We evaluate our algorithm experimentally by using it to learn, online, a schedule for allocating CPU time among solvers entered in the 2007 SAT solver competition.