Coding Schemes and Resource Allocations for The Multi-Task Coded Distributed Computation

Resource allocation for the multi-task coded distributed computation with limited computing and storage re-sources is considered. We first propose an optimal coding scheme and resource allocation strategy that achieve the minimum execution time for the single-task case. We then extend the coding scheme and allocation strategy to the multi-task case and present two scheduling strategies: first-input-first-output (FIFO) strategy and a linear programming (LP) based strategy. The FIFO strategy allocates the resources to the tasks in the order of arrival, and is easy to implement in many practical distributed computing systems such as Apache Spark. The LP-based strategy jointly designs resource allocation among all tasks, and can achieve shorter schedule makespan (the amount of time elapses from the start of the schedule to its end) than the FIFO strategy. Moreover, we prove that the LP-based strategy is robust that achieves the optimal makespan within a constant multiplicative gap, regardless of the system parameters.