Scaling long-context and agentic LLMs is increasingly limited by memory capacity and bandwidth rather than FLOPs. I propose an algorithmic framework for context engineering that models placement, compression, and scheduling as coupled optimization problems with explicit accuracy-efficiency trade-offs. Concretely, I will develop (1) salience-aware retention/eviction policies with provable approximation guarantees relative to an ideal oracle; (2) tier-dependent compression schemes that bound error propagation across memory levels; and (3) probabilistic prefetch/scheduling that controls tail latency. I will evaluate on long-context language modeling and reasoning benchmarks, isolating each component via ablations and comparing against heuristic baselines under controlled bandwidth/capacity regimes. Results target improved throughput and energy metrics at near-baseline quality, advancing principled, hardware-aware inference without requiring custom hardware.