Annals of Operations Research
Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties
On rectangle packing: maximizing benefits
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Hardness of approximation for orthogonal rectangle packing and covering problems
Journal of Discrete Algorithms
On efficient weighted rectangle packing with large resources
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
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The advertisement placement problem deals with space and time sharing by advertisements on the Internet. Consider a WWW 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 advertisements to appear simultaneously side by side, as well as by cycling through a schedule of ads, displaying different ads at different times. A customer wishing to purchase advertising space specifies an ad size and a display count, which is the number of times his advertisement should appear during each cycle. The scheduler may accept or reject any given advertisement, but must be able to schedule all accepted ones within the given time and space constraints, while honoring the display count of each. The objective is to schedule a maximumprofit subset of ads. We present a (3 + 驴)-approximation algorithm for the general problem, as well as (2+驴)-approximation algorithms for two special cases.