Approximating the advertisement placement problem

The advertisement placement problem deals with space and time sharing by advertisements on the Internet. Consider a Web page containing a rectangular display area (e.g., a banner) in which advertisements may appear. The display area can be utilized efficiently by allowing several small ads to appear simultaneously side by side, as well as by cycling through a schedule of ads, allowing different ads to be displayed at different times. A customer wishing to purchase advertising space specifies an ad size and a display count, which is the number of times their ad should appear during each cycle. The scheduler may accept or reject any given advertisement, but must be able to schedule all accepted ads within the given time and space constraints. Each advertisement has a non-negative profit associated with it, and the objective is to schedule a maximum-profit subset of ads. We present a (3 + ϵ)-approximation algorithm for the general problem, as well as (2 + ϵ)-approximation algorithms for two special cases.