Bounds on the client-server incremental computing

We discuss the problem of finding a dominating sequence for sending the input data items from a low-end client to a server for computational intensive tasks under the realistic assumption of unpredictable communication behaviors. Under the assumption, the client sends the input data items using a specified sequence to maximum the number of computations performed at the server at any moment. The sequence-finding problem is NP-hard for the general case. In this paper, we address two fundamental and useful applications: matrix multiplication and fast Fourier transform. We have shown that the sequence-finding problems of the applications can be solved optimally in linear time. However, we have also shown counter examples to rule out any possibility of finding a dominating sequence for the sparse cases. Finally, a simulation is conducted to show the correctness and usefulness of our results.