MEASURING THE PROBLEM-RELEVANTINFORMATION IN INPUT

We propose a new way of characterizing the complexity ofonline problems. Instead of measuring the degradation of the outputquality caused by the ignorance of the future we choose to quantifythe amount of additional global information needed for an online algorithmto solve the problem optimally. In our model, the algorithmcooperates with an oracle that can see the whole input. We definethe advice complexity of the problem to be the minimal number ofbits (normalized per input request, and minimized over all algorithmoraclepairs) communicated by the algorithm to the oracle in order tosolve the problem optimally. Hence, the advice complexity measuresthe amount of problem-relevant information contained in the input.We introduce two modes of communication between the algorithm andthe oracle based on whether the oracle offers an advice spontaneously(helper) or on request (answerer). We analyze the Paging and DiffServproblems in terms of advice complexity and deliver upper and lowerbounds in both communication modes; in the case of DiffServ problemin helper mode the bounds are tight