Approximation Algorithms for Dual-Memory Request Scheduling in Disaggregated LLM Inference

Disaggregated LLM inference executes the prefill and decode phases on separate resource pools, reducing interference between the two phases. However, this architecture introduces a coupled scheduling problem because a request that completes prefill retains its prompt KV cache in prefill memory until it is admitted to the decode pool. Prefill and decode admission decisions therefore jointly determine memory occupancy and request completion times. To the best of our knowledge, this problem lacks a formal formulation, and no approximation guarantees are known for request scheduling in disaggregated LLM inference. We formalize this setting as the dual-memory request scheduling (DMRS) problem, whose objective is to minimize the sum of request completion times, and prove that it is strongly NP-hard. We develop two deterministic polynomial-time approximation algorithms. The first applies to instances satisfying $\alpha <1$ and $\beta <1$ and achieves an approximation ratio of $8+\frac{4}{1-\alpha }+\frac{8}{1-\beta }$, where $\alpha$ and $\beta$ are the maximum normalized prefill and peak decode memory demands among all requests, respectively. In particular, it yields a $32$-approximation when $\alpha ,\beta \le 1/2$. The second algorithm applies to all feasible instances and achieves a uniform $36$-approximation. Finally, evaluations on two H100 GPUs using trace-derived offline workloads show that the proposed algorithms reduce the sum of request completion times relative to multiple vLLM deployment baselines.