Performance bounds of algorithms for scheduling advertisements on a web page

Consider a set of n advertisements (hereafter called "ads") A = {A1, . . . , An} competing to be placed in a planning horizon which is divided into N time intervals called slots. An ad Ai is specified by its size si and frequency wi. The size si represents the amount of space the ad occupies, in a slot. Ad Ai is said to be scheduled if exactly wi 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 A′ ⊆ A of ads such that the total occupied slot space ΣAi∈A′w isi maximized. We examine the complexity status of both problems and provide heuristics with performance guarantees.