New Online Algorithms for Story Scheduling in Web Advertising
Susanne Albers, Achim Passen · Algorithmica · 2018
We study storyboarding where advertisers wish to present sequences of ads (stories) uninterruptedly on a major ad position of a web page. These jobs/stories arrive online and are triggered by the browsing history of a user who at any time continues surfing with probability $$\beta $$ . The goal of an ad server is to construct a schedule maximizing the expected reward. The problem was introduced by Dasgupta, Ghosh, Nazerzadeh and Raghavan (SODA’09) who presented a 7-competitive online algorithm. They also showed that no deterministic online strategy can achieve a competitiveness smaller than 2, for general $$\beta $$ . We present improved algorithms for storyboarding. First we give a simple online strategy that achieves a competitive ratio of $$4/(2-\beta )$$ , which is upper bounded by 4 for any $$\beta $$ . The algorithm is also $$1/(1-\beta )$$ -competitive, which gives better bounds for small $$\beta $$ . As the main result of this paper we devise a refined algorithm that attains a competitive ratio of $$c=1+\phi $$ , where $$\phi =(1+\sqrt{5})/2$$ is the Golden Ratio. This performance guarantee of $$c\approx 2.618$$ is close to the lower bound of 2. Additionally, we study for the first time a problem extension where stories may be presented simultaneously on several ad positions of a web page. For this parallel setting we provide an algorithm whose competitive ratio is upper bounded by $$1/(3-2\sqrt{2})\approx 5.828$$ , for any $$\beta $$ . All our algorithms work in phases and have to make scheduling decisions only every once in a while.