ContextDAG: An Oracle Study of Dependency-Structured Context Selection for Multi-Topic LLM Conversations

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Conversations with large language models are usually served as one growing transcript, although users switch topics, return to earlier threads, and ask questions that depend on several threads at once. We study whether representing a conversation as a dependency DAG over turns, and building each request’s context from only the ancestor closure of the turns it depends on, can substantially reduce context while preserving answer quality. To separate the value of dependency-informed selection from the difficulty of inferring dependencies, we evaluate with an oracle router on a 145-scenario synthetic benchmark of 13 conversational patterns, with gold graphs fixed in code before any text was written and thresholds pre-registered before each phase’s first billed call. Across three response models, oracle DAG context uses 31% of full-history tokens and is non-inferior on checklist quality within a pre-registered −5 pp margin (paired differences +2.4 to +2.6 pp, every 95% interval including zero), while cutting token-weighted irrelevant context from 57% to 4% and judged distractor leakage from 14.5–18.6% to 2.1–2.8%. Against a turn-level embedding-retrieval baseline it is non-inferior at every budget tested up to 2.5× its tokens, retrieval is non-inferior to it at none, and its superiority is established only at matched budget on two of three models. Retaining multiple branches improves quality by about 32 pp over a single-parent tree on join scenarios. In a spliced length ablation, fixed-budget retrieval loses 14 points of context recall as history grows; the oracle’s margin over it is undetectable at base length, +12.0 pp [+4.4, +20.0] at 30 turns and +6.0 pp [−0.3, +12.7] at 60. We characterise four failure modes of turn-level selection, including retraction, in which a model shown only the gold turns disowns earlier assistant statements, and report that two constructions of longer synthetic conversations both produced easier tasks. This is an oracle study on synthetic data: it bounds what dependency-informed selection could be worth, does not separate the representation from knowing what to select, and its benchmark labels have not been independently audited. Total compute cost was $124; all artefacts are released.