Performance Bounds of Algorithms for Scheduling Advertisements on a Web Page

Consider a set of n advertisements (hereafter called ads) A ={A₁,...,A_n} competing to be placed in a planning horizon which is divided into N time intervals called slots. An ad A_i is specified by its size s_i and frequency w_i. The size s_i represents the amount of space the ad occupies in a slot. Ad A_i is said to be scheduled if exactly w_i copies of A_i are placed in the slots subject to the restriction that a slot contains at most one copy of an ad. In this paper, we consider two problems. The MINSPACE problem minimizes the maximum fullness among all slots in a feasible schedule where the fullness of a slot is the sum of the sizes of ads assigned to the slot. For the MAXSPACE problem, in addition, we are given a common maximum fullness S for all slots. The total size of the ads placed in a slot cannot exceed S. The objective is to find a feasible schedule of ads such that the total occupied slot space is maximized. We examine the complexity status of both problems and provide heuristics with performance guarantees.