Weighted Online Problems with Advice

Abstract

Abstract. Recently, the first online complexity class, AOC, was introduced. The class consists of many online problems where each request must be either accepted or rejected, and the aim is to either minimize or maximize the number of accepted requests, while maintaining a feasible solution. 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 significant difference in the advice complexity of complete minimization and maximization problems. We also show that our algorithmic techniques for dealing with weighted requests can be extended to work for non-complete AOC problems such as Matching in the edge arrival model (giving better results than what follow from the general AOC results) and even non-AOC problems such as scheduling.

Parallel solutions for preemptive makespan scheduling on two identical machines

“…The model with several solutions constructed in an online fashion is strongly related to online problems with advice. In such models, the algorithm has access to advice bits, which are hints telling the algorithm how to proceed [8,9,10]. The two models (with advice and with multiple solutions) are essentially equivalent.…”