New Online Algorithms for Story Scheduling in Web Advertising

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

β

. 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

β

.

We present improved algorithms for storyboarding. First we give a simple online strategy that achieves a competitive ratio of 4/(2 − 

β

), which is upper bounded by 4 for any

β

. The algorithm is also 1/(1 − 

β

)-competitive, which gives better bounds for small

β

. As the main result of this paper we devise a refined algorithm that attains a competitive ratio of

c

 = 1 + 

φ

, where

$\phi=(1+\sqrt{5})/2$

is the Golden Ratio. This performance guarantee of

c

 ≈ 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

β

. All our algorithms work in phases and have to make scheduling decisions only every once in a while.