The characterization of data-accumulating algorithms

Data-accumulating algorithms (d-algorithms for short), extensively studied in [12], work on an input considered as a virtually endless stream. The computation terminates when all the currently arrived data have been processed before another datum arrives. In this paper a finer characterization of the class of d-algorithms is given, and it is shown that this class is identical to the class of on-line algorithms under a proper definition of the latter. The parallel implementation of d-algorithms is then investigated. It is found that, in general, the speedup achieved through parallelism can be made arbitrarily large for almost any such algorithm. On the other hand, we prove that for d-algorithms whose static counterparts manifest only unitary speedup, no improvement is possible through parallel implementation.