Advice Complexity for a Class of Online Problems

Randomization can be as helpful as a glimpse of the future in online computation

“…If (S, T ) has max-cost ∆ then it follows from ( 28) that the cost incurred by any algorithm in a single round is at most ∆. Similarly, if (S, T ) has min-cost δ, then (29) ensures that if an online algorithm switches to a different state, then it incurs a cost of at least δ. The condition (30) ensures that if an online algorithm stays in the same state in some round, then it either incurs no cost at all or it incurs a cost of at least δ.…”

“…We will not consider the competitive ratio of a RMG-algorithm but instead the total cost incurred by the algorithm. Also, following previous work [48,24,29] on string guessing problems, we slightly abuse notation by using n to denote the number of input characters and not the number of requests, which is n + 1 (in the standard model of online problems, it is not possible to avoid this extra round since the ith input character must be revealed strictly later than when the algorithm has to output its ith character). Also, note that RMG does not have any initial state (n is not the initial state but a request that must be answered by the algorithm).…”

“…With a few notable exceptions (e.g. [24,48,25,29]), most of the previous research on advice complexity has been problem specific. In this paper, we take a more complexity-theoretic approach and focus on developing techniques that are applicable to many different problems.…”