Online Non-Preemptive Story Scheduling in Web Advertising

Tie-Yan Liu, Weidong Ma, Tao Qin, Pingzhong Tang, Guang Yang, Bo Zheng

Abstract: This paper is concerned with online story scheduling, motivated by storyboarding in online advertising. In storyboarding, triggered by the browsing history of a user, advertisers arrive online and wish to present a sequence of ads (stories) on the website. The user ceases to browse with probability 1-β at each time step. Once the user finishes watching an ad, the advertiser derives a reward. The goal of the website is to determine a schedule that maximizes the expected total reward. This problem was first introduced by Dasgupta et al.(SODA'09) [7], and then improved by Alberts and Passen (ICALP'13) [4]. In this paper, we abandon the preemptive assumption in [7] and [4], and consider a more realistic setting: online non-preemptive story scheduling, i.e., a running job (correspond to advertiser' story) cannot be preempted even if another job leads to a higher reward. Specifically, we study the setting where only 1-lengthed and k-lengthed ads are allowed. We first present a greedy algorithm which achieves a competitive ratio of βk-1, and prove that this ratio is optimal for deterministic algorithms. Then, we propose a randomized algorithm with a competitive ratio of 1 over k+1 for general β, and then show that no randomized algorithm can achieve a competitive ratio better than (1+(1-βk-1)kover(1-βk)k-1)-1.