Maximizing Sequence-Submodular Functions and Its Application to Online Advertising

Motivated by applications in online advertising, we consider a class of maximization problems where the objective is function sequence actions and running duration each action. For these problems, introduce concepts sequence-submodularity sequence-monotonicity, which extend notions submodularity monotonicity from functions defined over sets to sequences. We establish that if sequence-submodular sequence-nondecreasing, then there exists greedy algorithm achieves [Formula: see text] optimal solution. apply our analysis two advertising: ad allocation query rewriting. first show both can be formulated as maximizing nondecreasing functions. framework leading simple approaches with guaranteed performances. In particular, for problem, performance text], matches best known existing performance, rewriting improves on literature. This paper was accepted Chung Piaw Teo, optimization.