Recently, the first online complexity class, AOC, was introduced. The class consists of many online problems where each request must be either ac- cepted or rejected, and the aim is to either minimize or maximize the number of accepted requests, while maintaining a feasible solutio n. All AOC-complete problems (including Independent Set, Vertex Cover, Dominating Set, and Set Cover) have essentially the same advice complexity. In this paper, we study weighted versions of problems in AOC, i.e., each request comes with a weight and the aim is to either minimize or maximize the total weight of the accepted requests. In contrast to the unweighted versions, we show that there is a signif- icant difference in the advice complexity of complete minimization and max- imization problems. We also show that our algorithmic techniques for dealing with weighted requests can be extended to work for non-complete AOC prob- lems such as maximum matching (giving better results than what follow from the general AOC results) and even non-AOC problems such as scheduling.
['Joan Boyar', 'Lene M. Favrholdt', 'Christian Kudahl', 'Jesper W. Mikkelsen']
Weighted Online Problems with Advice