  Distributed computing, in which a resource-intensive task is divided into
subtasks and distributed among different machines, plays a key role in solving
large-scale problems. Coded computing is a recently emerging paradigm where
redundancy for distributed computing is introduced to alleviate the impact of
slow machines (stragglers) on the completion time. We investigate coded
computing solutions over elastic resources, where the set of available machines
may change in the middle of the computation. This is motivated by recently
available services in the cloud computing industry (e.g., EC2 Spot, Azure
Batch) where low-priority virtual machines are offered at a fraction of the
price of the on-demand instances but can be preempted on short notice. Our
contributions are three-fold. We first introduce a new concept called
transition waste that quantifies the number of tasks existing machines must
abandon or take over when a machine joins/leaves. We then develop an efficient
method to minimize the transition waste for the cyclic task allocation scheme
recently proposed in the literature (Yang et al. ISIT'19). Finally, we
establish a novel solution based on finite geometry achieving zero transition
wastes given that the number of active machines varies within a fixed range.
