Coded distributed computing (CDC) mitigates the Shuffle communication bottleneck through coded multicast, but existing schemes with predetermined worker populations do not directly adapt to worker arrivals and disconnections. To address these dynamics, we propose a dynamic CDC scheme that preserves surviving workers' caches and Reduce assignments while exploiting the storage brought by arriving clusters. The model accommodates general MapReduce tasks under a placement that is partly fixed and partly new. The scheme uses Cartesian products of cluster-wise placement delivery arrays (PDAs) for file placement. A delivery-aware greedy algorithm reassigns abandoned Reduce functions, and a Communication Array allows workers with no Reduce function to serve as coded transmitters. For arbitrary feasible disconnections, the scheme's exact communication load is derived. A converse bound under one-shot communication shows that, in the absence of disconnections, the scheme lies within a factor of 2 of the lower bound under these assumptions when new clusters arrive, and within a factor of 4 otherwise.

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