Alternatives to competitive analysis

Competitive analysis allows us to make strong theoretical statements about the performance of an algorithm without making probabilistic assumptions on the inputs. However, it has been often criticized with respect to its realism. A wide range of online algorithms –both good and not so good in practice– seem to have the same competitive ratio. A concrete example of this is the inability of competitive analysis to distinguish between the LRU and the FIFO algorithms for the paging problem, whose performances differ markedly in practice. (Recall that, on a fault, LRU evicts the page in memory whose most recent access was earliest, while FIFO evicts the page that has been in memory the longest). Moreover, competitive analysis frustrates not only interesting algorithms, but also information regimes. The classical example is again from paging. Suppose we allow a paging algorithm to have a lookahead of ` steps. Then, although we would expect better performance, the algorithm behaves equally badly as if it had no lookahead, as we’ll see later. The search for alternatives to competitive ratio is mainly driven by these weaknesses. The basic source of this problem is that quite often the best offline algorithm is too powerful to distinguish between online algorithm with different performance in practice. Different alternatives can be exploited to resolve this. The two obvious ways to generalize is to restrict the possible input distributions or/and the class of algorithms we compare the given online algorithm with. Before moving to such generalizations, recall the definition of competitive ratio of a minimization problem Π and of an algorithm for Π (for maxinization problems the definitions are analogous). Algorithm A is c-competitive if there exists a constant d, such that for any input x