Languages Alive

The recently introduced model of advice complexity of online problems tries to achieve a fine-grained analysis of the hardness of online problems by asking how many bits of advice about the still unknown parts of the input an oracle has to provide for an online algorithm to guarantee a specific competitive ratio. Until now, only deterministic online algorithms with advice were considered in the literature. In this paper, we consider, for the first time, online algorithms having access to both random bits and advice bits. For this, we introduce the online problem (n,k)-Boxes: Given a number of n closed boxes, an adversary hides \(k<\sqrt{n}\) items, each of unit value, within k consecutive boxes. The goal is to open exactly k boxes and gain as many items as possible.