Multi-user linearly-decomposable distributed computing

In this thesis, we explore the problem of multi-user linearly-decomposable distributed computing, where N servers help compute the desired functions (jobs) of K users, and where each desired function can be written as a linear combination of up to L (generally non-linear) subtasks (or sub-functions). Each server computes some of the subtasks, communicates a function of its computed outputs to some of the users, and then each user collects its received data to recover its desired function. We explore the computation, communication, and function reconstruction accuracy relationship by modeling the problem in finite fields and real numbers. We have established a firm theoretical bridge between multi-user linearly decomposable distributed computing and perfect or covering codes in finite fields. In the real field, it is shown that the communication, computation, and function reconstruction accuracy of this problem is related to the sparse matrix factorization and tessellation literature.