Maximizing Sequence-Submodular Functions and its Application to Online Advertising

In this paper we study a general class of online maximization problems which are as follows. We are given a time constraint T . We have to choose a sequence of actions from a set of possible actions and also the length of time to run each action subject to the total time being no more than T . Each action has a marginal profit. We show that if the problem has the following two properties, then there is a greedy algorithm that can yield O(1 − 1 e ) of the optimal. • Performing an action earlier does not decrease the marginal profit of the action. • Running a sequence of actions A followed by a sequence of actions B yields at least as much profit as the maximum profit of A or B. The greedy algorithm also has the advantage that it can still be applied in many settings where complete knowledge of the problem is not available or in online settings where the input is revealed gradually. We also give examples of non-trivial problems, for some of which we are not aware of any better algorithm. Dept. of Computer Science, University of Maryland, College Park, MD 20742. [email protected]. Dept. of Computer Science, University of Maryland, College Park, MD 20742. [email protected].